Spectral Shrinkage of Tyler's M-Estimator of Covariance Matrix

Arnaud Breloy, Esa Ollila, Frederic Pascal

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

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Abstract

Covariance matrices usually exhibit specific spectral structures, such as low-rank ones in the case of factor models. In order to exploit this prior knowledge in a robust estimation process, we propose a new regularized version of Tyler's M-estimator of covariance matrix. This estimator is expressed as the minimizer of a robust M -estimating cost function plus a penalty that is unitary invariant (i.e., that only applies on the eigenvalue) that shrinks the estimated spectrum toward a fixed target. The structure of the estimate is expressed through an interpretable fixed-point equation. A majorization-minimization (MM) algorithm is derived to compute this estimator, and the g-convexity of the objective is also discussed. Several simulation studies illustrate the interest of the approach and also explore a method to automatically choose the target spectrum through an auxiliary estimator.

Original languageEnglish
Title of host publication2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Proceedings
PublisherIEEE
Pages535-538
Number of pages4
ISBN (Electronic)9781728155494
DOIs
Publication statusPublished - 1 Dec 2019
MoE publication typeA4 Article in a conference publication
EventIEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing - Guadeloupe, Le Gosier, Guadeloupe
Duration: 15 Dec 201918 Dec 2019
https://camsap19.ig.umons.ac.be

Workshop

WorkshopIEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
Abbreviated titleCAMSAP
CountryGuadeloupe
CityLe Gosier
Period15/12/201918/12/2019
Internet address

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