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

Arnaud Breloy, Esa Ollila, Frederic Pascal

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference contributionScientificvertaisarvioitu

12 Lataukset (Pure)

Abstrakti

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.

AlkuperäiskieliEnglanti
Otsikko2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Proceedings
KustantajaIEEE
Sivut535-538
Sivumäärä4
ISBN (elektroninen)9781728155494
DOI - pysyväislinkit
TilaJulkaistu - 1 joulukuuta 2019
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisuussa
TapahtumaIEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing - Guadeloupe, Le Gosier, Guadeloupe
Kesto: 15 joulukuuta 201918 joulukuuta 2019
https://camsap19.ig.umons.ac.be

Workshop

WorkshopIEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
LyhennettäCAMSAP
MaaGuadeloupe
KaupunkiLe Gosier
Ajanjakso15/12/201918/12/2019
www-osoite

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