Estimation of autocovariance matrices for high dimensional linear processes
Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian cas...
Ausführliche Beschreibung
Gespeichert in:
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Furmańczyk, Konrad [verfasserIn] |
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E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Metrika - Berlin : Springer, 1958, 84(2020), 4 vom: 26. Aug., Seite 595-613 |
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| Übergeordnetes Werk: |
volume:84 ; year:2020 ; number:4 ; day:26 ; month:08 ; pages:595-613 |
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| DOI / URN: |
10.1007/s00184-020-00790-2 |
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| Katalog-ID: |
SPR043891934 |
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| 245 | 1 | 0 | |a Estimation of autocovariance matrices for high dimensional linear processes |
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| 520 | |a Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian case when %$p={\mathcal {O}}\left( n^{\gamma /2}\right) %$ for some %$\gamma >1%$, and in the general case when %$ p^{2/\beta }(n^{-1} \log p)^{1/2}\rightarrow 0%$ for some %$\beta >2%$ as %$ p=p(n)\rightarrow \infty %$ and the sample size %$n\rightarrow \infty %$. In particular our results hold for multivariate AR processes. We compare our results with those previously obtained in the literature for independent and dependent data. We also present non-asymptotic bounds for the error probability of these estimators. | ||
| 650 | 4 | |a High dimensional data |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Linear process |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Autocovariance matrix |7 (dpeaa)DE-He213 | |
| 773 | 0 | 8 | |i Enthalten in |t Metrika |d Berlin : Springer, 1958 |g 84(2020), 4 vom: 26. Aug., Seite 595-613 |w (DE-627)254630952 |w (DE-600)1462149-6 |x 1435-926X |7 nnns |
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| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00184-020-00790-2 |z kostenfrei |3 Volltext |
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10.1007/s00184-020-00790-2 doi (DE-627)SPR043891934 (DE-599)SPRs00184-020-00790-2-e (SPR)s00184-020-00790-2-e DE-627 ger DE-627 rakwb eng 510 310 ASE 510 ASE 31.73 bkl Furmańczyk, Konrad verfasserin aut Estimation of autocovariance matrices for high dimensional linear processes 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian case when %$p={\mathcal {O}}\left( n^{\gamma /2}\right) %$ for some %$\gamma >1%$, and in the general case when %$ p^{2/\beta }(n^{-1} \log p)^{1/2}\rightarrow 0%$ for some %$\beta >2%$ as %$ p=p(n)\rightarrow \infty %$ and the sample size %$n\rightarrow \infty %$. In particular our results hold for multivariate AR processes. We compare our results with those previously obtained in the literature for independent and dependent data. We also present non-asymptotic bounds for the error probability of these estimators. High dimensional data (dpeaa)DE-He213 Linear process (dpeaa)DE-He213 Autocovariance matrix (dpeaa)DE-He213 Enthalten in Metrika Berlin : Springer, 1958 84(2020), 4 vom: 26. Aug., Seite 595-613 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:84 year:2020 number:4 day:26 month:08 pages:595-613 https://dx.doi.org/10.1007/s00184-020-00790-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE AR 84 2020 4 26 08 595-613 |
| spelling |
10.1007/s00184-020-00790-2 doi (DE-627)SPR043891934 (DE-599)SPRs00184-020-00790-2-e (SPR)s00184-020-00790-2-e DE-627 ger DE-627 rakwb eng 510 310 ASE 510 ASE 31.73 bkl Furmańczyk, Konrad verfasserin aut Estimation of autocovariance matrices for high dimensional linear processes 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian case when %$p={\mathcal {O}}\left( n^{\gamma /2}\right) %$ for some %$\gamma >1%$, and in the general case when %$ p^{2/\beta }(n^{-1} \log p)^{1/2}\rightarrow 0%$ for some %$\beta >2%$ as %$ p=p(n)\rightarrow \infty %$ and the sample size %$n\rightarrow \infty %$. In particular our results hold for multivariate AR processes. We compare our results with those previously obtained in the literature for independent and dependent data. We also present non-asymptotic bounds for the error probability of these estimators. High dimensional data (dpeaa)DE-He213 Linear process (dpeaa)DE-He213 Autocovariance matrix (dpeaa)DE-He213 Enthalten in Metrika Berlin : Springer, 1958 84(2020), 4 vom: 26. Aug., Seite 595-613 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:84 year:2020 number:4 day:26 month:08 pages:595-613 https://dx.doi.org/10.1007/s00184-020-00790-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE AR 84 2020 4 26 08 595-613 |
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10.1007/s00184-020-00790-2 doi (DE-627)SPR043891934 (DE-599)SPRs00184-020-00790-2-e (SPR)s00184-020-00790-2-e DE-627 ger DE-627 rakwb eng 510 310 ASE 510 ASE 31.73 bkl Furmańczyk, Konrad verfasserin aut Estimation of autocovariance matrices for high dimensional linear processes 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian case when %$p={\mathcal {O}}\left( n^{\gamma /2}\right) %$ for some %$\gamma >1%$, and in the general case when %$ p^{2/\beta }(n^{-1} \log p)^{1/2}\rightarrow 0%$ for some %$\beta >2%$ as %$ p=p(n)\rightarrow \infty %$ and the sample size %$n\rightarrow \infty %$. In particular our results hold for multivariate AR processes. We compare our results with those previously obtained in the literature for independent and dependent data. We also present non-asymptotic bounds for the error probability of these estimators. High dimensional data (dpeaa)DE-He213 Linear process (dpeaa)DE-He213 Autocovariance matrix (dpeaa)DE-He213 Enthalten in Metrika Berlin : Springer, 1958 84(2020), 4 vom: 26. Aug., Seite 595-613 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:84 year:2020 number:4 day:26 month:08 pages:595-613 https://dx.doi.org/10.1007/s00184-020-00790-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE AR 84 2020 4 26 08 595-613 |
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10.1007/s00184-020-00790-2 doi (DE-627)SPR043891934 (DE-599)SPRs00184-020-00790-2-e (SPR)s00184-020-00790-2-e DE-627 ger DE-627 rakwb eng 510 310 ASE 510 ASE 31.73 bkl Furmańczyk, Konrad verfasserin aut Estimation of autocovariance matrices for high dimensional linear processes 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian case when %$p={\mathcal {O}}\left( n^{\gamma /2}\right) %$ for some %$\gamma >1%$, and in the general case when %$ p^{2/\beta }(n^{-1} \log p)^{1/2}\rightarrow 0%$ for some %$\beta >2%$ as %$ p=p(n)\rightarrow \infty %$ and the sample size %$n\rightarrow \infty %$. In particular our results hold for multivariate AR processes. We compare our results with those previously obtained in the literature for independent and dependent data. We also present non-asymptotic bounds for the error probability of these estimators. High dimensional data (dpeaa)DE-He213 Linear process (dpeaa)DE-He213 Autocovariance matrix (dpeaa)DE-He213 Enthalten in Metrika Berlin : Springer, 1958 84(2020), 4 vom: 26. Aug., Seite 595-613 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:84 year:2020 number:4 day:26 month:08 pages:595-613 https://dx.doi.org/10.1007/s00184-020-00790-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE AR 84 2020 4 26 08 595-613 |
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10.1007/s00184-020-00790-2 doi (DE-627)SPR043891934 (DE-599)SPRs00184-020-00790-2-e (SPR)s00184-020-00790-2-e DE-627 ger DE-627 rakwb eng 510 310 ASE 510 ASE 31.73 bkl Furmańczyk, Konrad verfasserin aut Estimation of autocovariance matrices for high dimensional linear processes 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian case when %$p={\mathcal {O}}\left( n^{\gamma /2}\right) %$ for some %$\gamma >1%$, and in the general case when %$ p^{2/\beta }(n^{-1} \log p)^{1/2}\rightarrow 0%$ for some %$\beta >2%$ as %$ p=p(n)\rightarrow \infty %$ and the sample size %$n\rightarrow \infty %$. In particular our results hold for multivariate AR processes. We compare our results with those previously obtained in the literature for independent and dependent data. We also present non-asymptotic bounds for the error probability of these estimators. High dimensional data (dpeaa)DE-He213 Linear process (dpeaa)DE-He213 Autocovariance matrix (dpeaa)DE-He213 Enthalten in Metrika Berlin : Springer, 1958 84(2020), 4 vom: 26. Aug., Seite 595-613 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:84 year:2020 number:4 day:26 month:08 pages:595-613 https://dx.doi.org/10.1007/s00184-020-00790-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE AR 84 2020 4 26 08 595-613 |
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Furmańczyk, Konrad |
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Furmańczyk, Konrad ddc 510 bkl 31.73 misc High dimensional data misc Linear process misc Autocovariance matrix Estimation of autocovariance matrices for high dimensional linear processes |
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510 310 ASE 510 ASE 31.73 bkl Estimation of autocovariance matrices for high dimensional linear processes High dimensional data (dpeaa)DE-He213 Linear process (dpeaa)DE-He213 Autocovariance matrix (dpeaa)DE-He213 |
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ddc 510 bkl 31.73 misc High dimensional data misc Linear process misc Autocovariance matrix |
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Estimation of autocovariance matrices for high dimensional linear processes |
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Estimation of autocovariance matrices for high dimensional linear processes |
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estimation of autocovariance matrices for high dimensional linear processes |
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Estimation of autocovariance matrices for high dimensional linear processes |
| abstract |
Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian case when %$p={\mathcal {O}}\left( n^{\gamma /2}\right) %$ for some %$\gamma >1%$, and in the general case when %$ p^{2/\beta }(n^{-1} \log p)^{1/2}\rightarrow 0%$ for some %$\beta >2%$ as %$ p=p(n)\rightarrow \infty %$ and the sample size %$n\rightarrow \infty %$. In particular our results hold for multivariate AR processes. We compare our results with those previously obtained in the literature for independent and dependent data. We also present non-asymptotic bounds for the error probability of these estimators. |
| abstractGer |
Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian case when %$p={\mathcal {O}}\left( n^{\gamma /2}\right) %$ for some %$\gamma >1%$, and in the general case when %$ p^{2/\beta }(n^{-1} \log p)^{1/2}\rightarrow 0%$ for some %$\beta >2%$ as %$ p=p(n)\rightarrow \infty %$ and the sample size %$n\rightarrow \infty %$. In particular our results hold for multivariate AR processes. We compare our results with those previously obtained in the literature for independent and dependent data. We also present non-asymptotic bounds for the error probability of these estimators. |
| abstract_unstemmed |
Abstract In this paper under some mild restrictions upper bounds on the rate of convergence for estimators of %$p\times p%$ autocovariance and precision matrices for high dimensional linear processes are given. We show that these estimators are consistent in the operator norm in the sub-Gaussian case when %$p={\mathcal {O}}\left( n^{\gamma /2}\right) %$ for some %$\gamma >1%$, and in the general case when %$ p^{2/\beta }(n^{-1} \log p)^{1/2}\rightarrow 0%$ for some %$\beta >2%$ as %$ p=p(n)\rightarrow \infty %$ and the sample size %$n\rightarrow \infty %$. In particular our results hold for multivariate AR processes. We compare our results with those previously obtained in the literature for independent and dependent data. We also present non-asymptotic bounds for the error probability of these estimators. |
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| title_short |
Estimation of autocovariance matrices for high dimensional linear processes |
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https://dx.doi.org/10.1007/s00184-020-00790-2 |
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10.1007/s00184-020-00790-2 |
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2024-07-03T21:35:24.452Z |
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