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

School of Arts and Sciences, Statistics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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 (US)
Pages (from-to)	80-85
Number of pages	6
Journal	Statistics and Probability Letters
Volume	111
DOIs	https://doi.org/10.1016/j.spl.2016.01.009
State	Published - Apr 1 2016

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Elliptical distribution
Spatial Kendall's tau matrix
Spatial sign

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10.1016/j.spl.2016.01.009

Cite this

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title = "On the eigenvalues of the spatial sign covariance matrix in more than two dimensions",

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.",

keywords = "Elliptical distribution, Spatial Kendall's tau matrix, Spatial sign",

author = "Alexander D{\"u}rre and Tyler, {David E.} and Daniel Vogel",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

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doi = "10.1016/j.spl.2016.01.009",

language = "English (US)",

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T1 - On the eigenvalues of the spatial sign covariance matrix in more than two dimensions

AU - Dürre, Alexander

AU - Tyler, David E.

AU - Vogel, Daniel

N1 - Funding Information: 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. Publisher Copyright: © 2016 Elsevier B.V.

PY - 2016/4/1

Y1 - 2016/4/1

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 - Elliptical distribution

KW - Spatial Kendall's tau matrix

KW - Spatial sign

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M3 - Article

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SN - 0167-7152

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

All Science Journal Classification (ASJC) codes

Keywords

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