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Activity Number: 361
Type: Contributed
Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #309166
Title: James-Stein Estimation for P Bigger Than N and Unknown Covariance Matrix
Author(s): Didier Chetelat*+ and Martin T Wells
Companies: Cornell University and Cornell University
Keywords: James-Stein ; large-p-small-n ; high dimension ; minimax ; covariance
Abstract:

We consider the problem of estimating the mean vector of a p- variate normal distribution under invariant quadratic loss when the covariance is unknown. In the spirit of the classical James-Stein estimator, we propose a new class of estimators that dominate the trivial estimator X. The proposed estimators depend upon X and an independent Wishart matrix S with n degrees of freedom, even though such a matrix is almost surely singular for p > n. The proof of domination involves the development of some new unbiased estimators of risk for such a setting. In the process, we also exhibit relationships between the amount of domination and the magnitudes of n and p.


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