Tyler's estimator performance analysis

Ilya Soloveychik, Ami Wiesel

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

This paper analyzes the performance of Tyler's M-estimator of the scatter matrix in elliptical populations. We focus on non-asymptotic performance analysis of Tyler's estimator. Given n samples of dimension p < n, we show that the squared Frobenius norm of the error of the inverse estimator is proportional to p2/(1-c2)2n with high probability, where c is the coherence coefficient of the properly scaled estimator. Under additional group symmetry conditions we improve the obtained bound, utilizing the inherent sparsity properties of group symmetry.

Original languageAmerican English
Title of host publication2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5688-5692
Number of pages5
ISBN (Electronic)9781467369978
DOIs
StatePublished - 4 Aug 2015
Event40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia
Duration: 19 Apr 201424 Apr 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2015-August
ISSN (Print)1520-6149

Conference

Conference40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
Country/TerritoryAustralia
CityBrisbane
Period19/04/1424/04/14

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Keywords

  • Elliptical distribution shape matrix estimation
  • Tyler's scatter estimator
  • concentration bounds
  • scatter matrix M-estimators

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