Covariance estimation in elliptical models with convex structure

Ilya Soloveychik, Ami Wiesel

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

Abstract

We develop the General Method of Moments (GMM) Approach for estimating the covariance matrices of non-Gaussian distributions with convex structure. The GMM turns out to be a non-convex optimization problem, thus making the addition of prior knowledge in form of convex structure constraints cumbersome. We propose a different approach to this estimator and show that the Tyler's estimator can be obtained as a solution of a convexly relaxed GMM problem, thus making the imposition of convex constraints easier. This new framework provides consistent solutions which outperform the standard projection methods. As an application of this method we consider Gaussian Compound samples with Toeplitz and banded covariance matrices. We provide synthetic numerical data and demonstrate the performance advantages of our method.

Original languageAmerican English
Title of host publication2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5646-5650
Number of pages5
ISBN (Print)9781479928927
DOIs
StatePublished - 2014
Event2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 - Florence, Italy
Duration: 4 May 20149 May 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Conference

Conference2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
Country/TerritoryItaly
CityFlorence
Period4/05/149/05/14

Keywords

  • Elliptical distribution
  • Generalized Method of Moments
  • Tyler's scatter estimator
  • non-Gaussian constrained covariance estimation

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