Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET
Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</...
Ausführliche Beschreibung
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| Autor*in: |
Innocent Mudhombo [verfasserIn] Edmore Ranganai [verfasserIn] |
|---|
| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
In: Computation - MDPI AG, 2014, 10(2022), 11, p 203 |
|---|---|
| Übergeordnetes Werk: |
volume:10 ; year:2022 ; number:11, p 203 |
| Links: |
|---|
| DOI / URN: |
10.3390/computation10110203 |
|---|
| Katalog-ID: |
DOAJ085595357 |
|---|
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| 041 | |a eng | ||
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| 100 | 0 | |a Innocent Mudhombo |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET |
| 264 | 1 | |c 2022 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 520 | |a Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<... | ||
| 650 | 4 | |a weighted quantile regression | |
| 650 | 4 | |a adaptive LASSO penalty | |
| 650 | 4 | |a penalty | |
| 650 | 4 | |a adaptive E-NET penalty | |
| 650 | 4 | |a collinearity inducing point | |
| 650 | 4 | |a collinearity hiding point | |
| 653 | 0 | |a Electronic computers. Computer science | |
| 700 | 0 | |a Edmore Ranganai |e verfasserin |4 aut | |
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10.3390/computation10110203 doi (DE-627)DOAJ085595357 (DE-599)DOAJ09f8c680392e422da203d67130bf4f04 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Innocent Mudhombo verfasserin aut Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<... weighted quantile regression adaptive LASSO penalty penalty adaptive E-NET penalty collinearity inducing point collinearity hiding point Electronic computers. Computer science Edmore Ranganai verfasserin aut In Computation MDPI AG, 2014 10(2022), 11, p 203 (DE-627)751861367 (DE-600)2723192-6 20793197 nnns volume:10 year:2022 number:11, p 203 https://doi.org/10.3390/computation10110203 kostenfrei https://doaj.org/article/09f8c680392e422da203d67130bf4f04 kostenfrei https://www.mdpi.com/2079-3197/10/11/203 kostenfrei https://doaj.org/toc/2079-3197 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 11, p 203 |
| spelling |
10.3390/computation10110203 doi (DE-627)DOAJ085595357 (DE-599)DOAJ09f8c680392e422da203d67130bf4f04 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Innocent Mudhombo verfasserin aut Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<... weighted quantile regression adaptive LASSO penalty penalty adaptive E-NET penalty collinearity inducing point collinearity hiding point Electronic computers. Computer science Edmore Ranganai verfasserin aut In Computation MDPI AG, 2014 10(2022), 11, p 203 (DE-627)751861367 (DE-600)2723192-6 20793197 nnns volume:10 year:2022 number:11, p 203 https://doi.org/10.3390/computation10110203 kostenfrei https://doaj.org/article/09f8c680392e422da203d67130bf4f04 kostenfrei https://www.mdpi.com/2079-3197/10/11/203 kostenfrei https://doaj.org/toc/2079-3197 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 11, p 203 |
| allfields_unstemmed |
10.3390/computation10110203 doi (DE-627)DOAJ085595357 (DE-599)DOAJ09f8c680392e422da203d67130bf4f04 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Innocent Mudhombo verfasserin aut Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<... weighted quantile regression adaptive LASSO penalty penalty adaptive E-NET penalty collinearity inducing point collinearity hiding point Electronic computers. Computer science Edmore Ranganai verfasserin aut In Computation MDPI AG, 2014 10(2022), 11, p 203 (DE-627)751861367 (DE-600)2723192-6 20793197 nnns volume:10 year:2022 number:11, p 203 https://doi.org/10.3390/computation10110203 kostenfrei https://doaj.org/article/09f8c680392e422da203d67130bf4f04 kostenfrei https://www.mdpi.com/2079-3197/10/11/203 kostenfrei https://doaj.org/toc/2079-3197 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 11, p 203 |
| allfieldsGer |
10.3390/computation10110203 doi (DE-627)DOAJ085595357 (DE-599)DOAJ09f8c680392e422da203d67130bf4f04 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Innocent Mudhombo verfasserin aut Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<... weighted quantile regression adaptive LASSO penalty penalty adaptive E-NET penalty collinearity inducing point collinearity hiding point Electronic computers. Computer science Edmore Ranganai verfasserin aut In Computation MDPI AG, 2014 10(2022), 11, p 203 (DE-627)751861367 (DE-600)2723192-6 20793197 nnns volume:10 year:2022 number:11, p 203 https://doi.org/10.3390/computation10110203 kostenfrei https://doaj.org/article/09f8c680392e422da203d67130bf4f04 kostenfrei https://www.mdpi.com/2079-3197/10/11/203 kostenfrei https://doaj.org/toc/2079-3197 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 11, p 203 |
| allfieldsSound |
10.3390/computation10110203 doi (DE-627)DOAJ085595357 (DE-599)DOAJ09f8c680392e422da203d67130bf4f04 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Innocent Mudhombo verfasserin aut Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<... weighted quantile regression adaptive LASSO penalty penalty adaptive E-NET penalty collinearity inducing point collinearity hiding point Electronic computers. Computer science Edmore Ranganai verfasserin aut In Computation MDPI AG, 2014 10(2022), 11, p 203 (DE-627)751861367 (DE-600)2723192-6 20793197 nnns volume:10 year:2022 number:11, p 203 https://doi.org/10.3390/computation10110203 kostenfrei https://doaj.org/article/09f8c680392e422da203d67130bf4f04 kostenfrei https://www.mdpi.com/2079-3197/10/11/203 kostenfrei https://doaj.org/toc/2079-3197 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 11, p 203 |
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In Computation 10(2022), 11, p 203 volume:10 year:2022 number:11, p 203 |
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In Computation 10(2022), 11, p 203 volume:10 year:2022 number:11, p 203 |
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weighted quantile regression adaptive LASSO penalty penalty adaptive E-NET penalty collinearity inducing point collinearity hiding point Electronic computers. Computer science |
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Innocent Mudhombo @@aut@@ Edmore Ranganai @@aut@@ |
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2022-01-01T00:00:00Z |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">DOAJ085595357</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240414170418.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230311s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.3390/computation10110203</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ085595357</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJ09f8c680392e422da203d67130bf4f04</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA75.5-76.95</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">Innocent Mudhombo</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<...</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">weighted quantile regression</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">adaptive LASSO penalty</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">penalty</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">adaptive E-NET penalty</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">collinearity inducing point</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">collinearity hiding point</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Electronic computers. 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Innocent Mudhombo misc QA75.5-76.95 misc weighted quantile regression misc adaptive LASSO penalty misc penalty misc adaptive E-NET penalty misc collinearity inducing point misc collinearity hiding point misc Electronic computers. Computer science Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET |
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QA75.5-76.95 Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET weighted quantile regression adaptive LASSO penalty penalty adaptive E-NET penalty collinearity inducing point collinearity hiding point |
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misc QA75.5-76.95 misc weighted quantile regression misc adaptive LASSO penalty misc penalty misc adaptive E-NET penalty misc collinearity inducing point misc collinearity hiding point misc Electronic computers. Computer science |
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misc QA75.5-76.95 misc weighted quantile regression misc adaptive LASSO penalty misc penalty misc adaptive E-NET penalty misc collinearity inducing point misc collinearity hiding point misc Electronic computers. Computer science |
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Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET |
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robust variable selection and regularization in quantile regression based on adaptive-lasso and adaptive e-net |
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QA75.5-76.95 |
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Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET |
| abstract |
Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<... |
| abstractGer |
Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<... |
| abstract_unstemmed |
Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<... |
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| container_issue |
11, p 203 |
| title_short |
Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET |
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https://doi.org/10.3390/computation10110203 https://doaj.org/article/09f8c680392e422da203d67130bf4f04 https://www.mdpi.com/2079-3197/10/11/203 https://doaj.org/toc/2079-3197 |
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Edmore Ranganai |
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Edmore Ranganai |
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QA - Mathematics |
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10.3390/computation10110203 |
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2024-07-03T15:42:55.956Z |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">DOAJ085595357</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240414170418.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230311s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.3390/computation10110203</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ085595357</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJ09f8c680392e422da203d67130bf4f04</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA75.5-76.95</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">Innocent Mudhombo</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<Q</mi<<mi<R</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (<i<X</i<-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and adaptive <i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures where the weights are based on a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< estimator as remedies. We extend this methodology to their penalized weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< versions of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<R</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<) parameter estimator. Although the use of this estimator may be plausible at the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msub<<mo<ℓ</mo<<mn<1</mn<</msub<</semantics<</math<</inline-formula< estimator (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< at <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<τ</mi<<mo<=</mo<<mn<0.5</mn<</mrow<</semantics<</math<</inline-formula<) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-based estimator to derive adaptive weights. We carried out a comparative study of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<i<E</i<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, and the ones we suggest here, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<v</mi<<mi<i</mi<<mi<z</mi<<mo<.</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<, weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< penalized and weighted <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula< adaptive <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula< penalized (<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<W</mi<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mi<E</mi<<mi<T</mi<</mrow<</semantics<</math<</inline-formula<) procedures. The simulation study results show that <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<L</mi<<mi<A</mi<<mi<S</mi<<mi<S</mi<<mi<O</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mi<R</mi<</mrow<</semantics<</math<</inline-formula<-<inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<A</mi<<mi<E<...</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">weighted quantile regression</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">adaptive LASSO penalty</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">penalty</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">adaptive E-NET penalty</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">collinearity inducing point</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">collinearity hiding point</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Electronic computers. 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