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

Thumbnail Image

Access rights

openAccess

URL

Journal Title

Journal ISSN

Volume Title

A4 Artikkeli konferenssijulkaisussa
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)

Authors

Date

2019-12-01

Department

Department of Signal Processing and Acoustics

Major/Subject

Mcode

Degree programme

Language

en

Pages

4
535-538

Series

2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Proceedings

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.

Description

Keywords

Other note

DOI

10.1109/CAMSAP45676.2019.9022652

Citation

Breloy, A, Ollila, E & Pascal, F 2019, Spectral Shrinkage of Tyler's M-Estimator of Covariance Matrix . in 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Proceedings ., 9022652, IEEE, pp. 535-538, IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Le Gosier, Guadeloupe, 15/12/2019 . https://doi.org/10.1109/CAMSAP45676.2019.9022652

Permanent link to this item

https://urn.fi/URN:NBN:fi:aalto-202004282937

Collections

[article-cris] Sähkötekniikan korkeakoulu / ELEC