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 journalArticlepeer-review

15 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 languageEnglish (US)
Pages (from-to)80-85
Number of pages6
JournalStatistics and Probability Letters
Volume111
DOIs
StatePublished - 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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