Robust shrinkage estimation of high-dimensional covariance matrices

Yilun Chen*, Ami Wiesel, Alfred O. Hero

*Corresponding author for this work

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

13 Scopus citations

Abstract

We address high dimensional covariance estimation for elliptical distributed samples. Specifically we consider shrinkage methods that are suitable for high dimensional problems with a small number of samples (large p small n). We start from a classical robust covariance estimator [Tyler(1987)], which is distribution-free within the family of elliptical distribution but inapplicable when n < p. Using a shrinkage coefficient, we regularize Tyler's fixed point iteration. We derive the minimum mean-squared-error shrinkage coefficient in closed form. The closed form expression is a function of the unknown true covariance and cannot be implemented in practice. Instead, we propose a plug-in estimate to approximate it. Simulations demonstrate that the proposed method achieves low estimation error and is robust to heavy-tailed samples.

Original languageEnglish
Title of host publication2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010
Pages189-192
Number of pages4
DOIs
StatePublished - 2010
Event2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010 - Jerusalem, Israel
Duration: 4 Oct 20107 Oct 2010

Publication series

Name2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010

Conference

Conference2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010
Country/TerritoryIsrael
CityJerusalem
Period4/10/107/10/10

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