On the eigenvalues of the spatial sign covariance matrix in more than two dimensions

Alexander Dürre; David E. Tyler; Daniel Vogel

doi:10.1016/j.spl.2016.01.009

On the eigenvalues of the spatial sign covariance matrix in more than two dimensions

Alexander Dürre, David E. Tyler, Daniel Vogel

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Abstract

We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer together than the latter. We further provide a one-dimensional integral representation of the eigenvalues, which facilitates their numerical computation.

Original language	English
Pages (from-to)	80-85
Number of pages	6
Journal	Statistics and Probability Letters
Volume	111
Early online date	21 Jan 2016
DOIs	https://doi.org/10.1016/j.spl.2016.01.009
Publication status	Published - Apr 2016

Bibliographical note

Acknowledgments
Alexander Dürre was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. David E. Tyler was supported in part by the National Science Foundation grant DMS-1407751. A visit of Daniel Vogel to David E. Tyler was supported by a travel grant from the Scottish Universities Physics Alliance. The authors are grateful to the editors and referees for their constructive comments.

Keywords

62H12
62G20
62H11
Elliptical distribution
Spatial Kendall’s tau matrix
spatial sign covariance matrix

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© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 281 KBLicence: CC BY-NC-ND

Cite this

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note = "Acknowledgments Alexander D{\"u}rre was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. David E. Tyler was supported in part by the National Science Foundation grant DMS-1407751. A visit of Daniel Vogel to David E. Tyler was supported by a travel grant from the Scottish Universities Physics Alliance. The authors are grateful to the editors and referees for their constructive comments.",

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AU - Dürre, Alexander

AU - Tyler, David E.

AU - Vogel, Daniel

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PY - 2016/4

Y1 - 2016/4

N2 - We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer together than the latter. We further provide a one-dimensional integral representation of the eigenvalues, which facilitates their numerical computation.

AB - We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer together than the latter. We further provide a one-dimensional integral representation of the eigenvalues, which facilitates their numerical computation.

KW - 62H12

KW - 62G20

KW - 62H11

KW - Elliptical distribution

KW - Spatial Kendall’s tau matrix

KW - spatial sign covariance matrix

U2 - 10.1016/j.spl.2016.01.009

DO - 10.1016/j.spl.2016.01.009

M3 - Article

VL - 111

SP - 80

EP - 85

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

On the eigenvalues of the spatial sign covariance matrix in more than two dimensions

Abstract

Bibliographical note

Keywords

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