NDLI: Tyler's Covariance Matrix Estimator in Elliptical Models With Convex Structure

Content Provider	IEEE Xplore Digital Library
Author	Soloveychik, I. Wiesel, A.
Copyright Year	1991
Abstract	We address structured covariance estimation in elliptical distributions by assuming that the covariance is a priori known to belong to a given convex set, e.g., the set of Toeplitz or banded matrices. We consider the General Method of Moments (GMM) optimization applied to robust Tyler's scatter M-estimator subject to these convex constraints. Unfortunately, GMM turns out to be non-convex due to the objective. Instead, we propose a new COCA estimator-a convex relaxation which can be efficiently solved. We prove that the relaxation is tight in the unconstrained case for a finite number of samples, and in the constrained case asymptotically. We then illustrate the advantages of COCA in synthetic simulations with structured compound Gaussian distributions. In these examples, COCA outperforms competing methods such as Tyler's estimator and its projection onto the structure set.
Sponsorship	IEEE Signal Processing Society
Starting Page	5251
Ending Page	5259
Page Count	9
File Size	1721109
File Format	PDF
ISSN	1053587X
Volume Number	62
Issue Number	20
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Covariance matrices Vectors Estimation Shape Bismuth Computer aided engineering Robustness robust covariance estimation Elliptical distribution Tyler's scatter estimator generalized method of moments
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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