Multivariate Empirical Bayes and Estimation of Covariance Matrices

by Bradley Efron, Carl N. Morris

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The authors consider the problem of estimating a covariance matrix in the standard multivariate normal situation. The loss function is one obtained naturally from the problem of estimating several normal mean vectors in an empirical Bayes situation. Estimators which dominate any constant multiple of the sample covariance matrix are presented. These estimators work by shrinking the sample eigenvalues toward a central value, in much the same way as the James-Stein estimator for a mean vector shrinks the maximum likelihood estimators toward a common value. (For publication in the Annals of Statistics.)

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