M-estimators of scatter with eigenvalue shrinkage

Esa Ollila, Daniel P. Palomar, Frédéric Pascal

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

1 Citation (Scopus)
143 Downloads (Pure)

Abstract

A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general approach is considered in which the SCM is replaced by an M-estimator of scatter matrix and a fully automatic data adaptive method to compute the optimal shrinkage parameter with minimum mean squared error is proposed. Our approach permits the use of any weight function such as Gaussian, Huber's, or t weight functions, all of which are commonly used in M-estimation framework. Our simulation examples illustrate that shrinkage M-estimators based on the proposed optimal tuning combined with robust weight function do not loose in performance to shrinkage SCM estimator when the data is Gaussian, but provide significantly improved performance when the data is sampled from a heavy-tailed distribution.

Original languageEnglish
Title of host publication2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings
PublisherIEEE
Pages5305-5309
Number of pages5
ISBN (Electronic)9781509066315
DOIs
Publication statusPublished - May 2020
MoE publication typeA4 Conference publication
EventIEEE International Conference on Acoustics, Speech, and Signal Processing - Virtual conference, Barcelona, Spain
Duration: 4 May 20208 May 2020
Conference number: 45

Publication series

NameProceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
ISSN (Print)1520-6149
ISSN (Electronic)2379-190X

Conference

ConferenceIEEE International Conference on Acoustics, Speech, and Signal Processing
Abbreviated titleICASSP
Country/TerritorySpain
CityBarcelona
Period04/05/202008/05/2020
OtherVirtual conference

Keywords

  • Elliptical distributions
  • M-estimators
  • Regularization
  • Sample covariance matrix
  • Shrinkage

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