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

40 Scopus citations

Abstract

We address covariance estimation under mean-squared loss in the Gaussian setting. Specifically, we consider shrinkage methods which are suitable for high dimensional problems with small number of samples (large p small n). First, we improve on the Ledoit-Wolf (LW) method by conditioning on a sufficient statistic via the Rao-Blackwell theorem, obtaining a new estimator RBLW whose mean-squared error dominates the LW under Gaussian model. Second, to further reduce the estimation error, we propose an iterative approach which approximates the clairvoyant shrinkage estimator. Convergence of this iterative method is proven and a closed form expression for the limit is determined, which is called the OAS estimator. Both of the proposed estimators have simple expressions and are easy to compute. Although the two methods are developed from different approaches, their structure is identical up to specific constants. The RBLW estimator provably dominates the LW method; and numerical simulations demonstrate that the OAS estimator performs even better, especially when n is much less than p.

Original languageAmerican English
Title of host publication2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009
Pages2937-2940
Number of pages4
DOIs
StatePublished - 2009
Externally publishedYes
Event2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009 - Taipei, Taiwan, Province of China
Duration: 19 Apr 200924 Apr 2009

Publication series

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

Conference

Conference2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009
Country/TerritoryTaiwan, Province of China
CityTaipei
Period19/04/0924/04/09

Keywords

  • Covariance estimation
  • Mean-squared loss
  • Rao-Blackwell
  • Shrinkage

Fingerprint

Dive into the research topics of 'Shrinkage estimation of high dimensional covariance matrices'. Together they form a unique fingerprint.

Cite this