Tyler's Covariance Matrix Estimator in Elliptical Models with Convex Structure

Ilya Soloveychik, Ami Wiesel

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40 Scopus citations


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.

Original languageAmerican English
Article number6879458
Pages (from-to)5251-5259
Number of pages9
JournalIEEE Transactions on Signal Processing
Issue number20
StatePublished - 15 Oct 2014

Bibliographical note

Publisher Copyright:
© 2014 IEEE.


  • Elliptical distribution
  • Tyler's scatter estimator
  • generalized method of moments
  • robust covariance estimation


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