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ICASSP
2009
IEEE

Shrinkage estimation of high dimensional covariance matrices

10 years 4 months ago
Shrinkage estimation of high dimensional covariance matrices
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 LedoitWolf (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 proved 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...
Yilun Chen, Ami Wiesel, Alfred O. Hero
Added 21 May 2010
Updated 21 May 2010
Type Conference
Year 2009
Where ICASSP
Authors Yilun Chen, Ami Wiesel, Alfred O. Hero
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