Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation
Abstract In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Aerts, S. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Statistical papers - Springer Berlin Heidelberg, 1988, 59(2016), 2 vom: 21. Mai, Seite 545-579 |
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| Übergeordnetes Werk: |
volume:59 ; year:2016 ; number:2 ; day:21 ; month:05 ; pages:545-579 |
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10.1007/s00362-016-0777-4 |
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| 520 | |a Abstract In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations. | ||
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10.1007/s00362-016-0777-4 doi (DE-627)OLC2025028121 (DE-He213)s00362-016-0777-4-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Aerts, S. verfasserin aut Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations. Multivariate coefficient of variation Bias reduction Decentralized -distribution Elliptical symmetry Sharpe Ratio Haesbroeck, G. aut Ruwet, C. aut Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 59(2016), 2 vom: 21. Mai, Seite 545-579 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:59 year:2016 number:2 day:21 month:05 pages:545-579 https://doi.org/10.1007/s00362-016-0777-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_26 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2018 GBV_ILN_4046 GBV_ILN_4277 GBV_ILN_4319 GBV_ILN_4326 AR 59 2016 2 21 05 545-579 |
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10.1007/s00362-016-0777-4 doi (DE-627)OLC2025028121 (DE-He213)s00362-016-0777-4-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Aerts, S. verfasserin aut Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations. Multivariate coefficient of variation Bias reduction Decentralized -distribution Elliptical symmetry Sharpe Ratio Haesbroeck, G. aut Ruwet, C. aut Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 59(2016), 2 vom: 21. Mai, Seite 545-579 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:59 year:2016 number:2 day:21 month:05 pages:545-579 https://doi.org/10.1007/s00362-016-0777-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_26 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2018 GBV_ILN_4046 GBV_ILN_4277 GBV_ILN_4319 GBV_ILN_4326 AR 59 2016 2 21 05 545-579 |
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10.1007/s00362-016-0777-4 doi (DE-627)OLC2025028121 (DE-He213)s00362-016-0777-4-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Aerts, S. verfasserin aut Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations. Multivariate coefficient of variation Bias reduction Decentralized -distribution Elliptical symmetry Sharpe Ratio Haesbroeck, G. aut Ruwet, C. aut Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 59(2016), 2 vom: 21. Mai, Seite 545-579 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:59 year:2016 number:2 day:21 month:05 pages:545-579 https://doi.org/10.1007/s00362-016-0777-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_26 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2018 GBV_ILN_4046 GBV_ILN_4277 GBV_ILN_4319 GBV_ILN_4326 AR 59 2016 2 21 05 545-579 |
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10.1007/s00362-016-0777-4 doi (DE-627)OLC2025028121 (DE-He213)s00362-016-0777-4-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Aerts, S. verfasserin aut Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations. Multivariate coefficient of variation Bias reduction Decentralized -distribution Elliptical symmetry Sharpe Ratio Haesbroeck, G. aut Ruwet, C. aut Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 59(2016), 2 vom: 21. Mai, Seite 545-579 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:59 year:2016 number:2 day:21 month:05 pages:545-579 https://doi.org/10.1007/s00362-016-0777-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_26 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2018 GBV_ILN_4046 GBV_ILN_4277 GBV_ILN_4319 GBV_ILN_4326 AR 59 2016 2 21 05 545-579 |
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Abstract In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations. © Springer-Verlag Berlin Heidelberg 2016 |
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Abstract In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations. © Springer-Verlag Berlin Heidelberg 2016 |
| abstract_unstemmed |
Abstract In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations. © Springer-Verlag Berlin Heidelberg 2016 |
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| title_short |
Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation |
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https://doi.org/10.1007/s00362-016-0777-4 |
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Haesbroeck, G. Ruwet, C. |
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