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

Alexander Dürre, David E. Tyler, Daniel Vogel

Research output: Contribution to journalArticle

3 Citations (Scopus)
4 Downloads (Pure)

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 languageEnglish
Pages (from-to)80-85
Number of pages6
JournalStatistics and Probability Letters
Volume111
Early online date21 Jan 2016
DOIs
Publication statusPublished - Apr 2016

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Covariance matrix
Two Dimensions
Eigenvalue
Elliptical Distribution
Integral Representation
Numerical Computation
Eigenvalues

Keywords

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

Cite this

On the eigenvalues of the spatial sign covariance matrix in more than two dimensions. / Dürre, Alexander; Tyler, David E.; Vogel, Daniel.

In: Statistics and Probability Letters, Vol. 111, 04.2016, p. 80-85.

Research output: Contribution to journalArticle

Dürre, Alexander ; Tyler, David E. ; Vogel, Daniel. / On the eigenvalues of the spatial sign covariance matrix in more than two dimensions. In: Statistics and Probability Letters. 2016 ; Vol. 111. pp. 80-85.
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