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January, 1976 Multivariate Empirical Bayes and Estimation of Covariance Matrices
Bradley Efron, Carl Morris
Ann. Statist. 4(1): 22-32 (January, 1976). DOI: 10.1214/aos/1176343345


The problem of estimating several normal mean vectors in an empirical Bayes situation is considered. In this case, it reduces to the problem of estimating the inverse of a covariance matrix in the standard multivariate normal situation using a particular loss function. Estimators which dominate any constant multiple of the inverse 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. These covariance estimators then lead to a class of multivariate estimators of the mean, each of which dominates the maximum likelihood estimator.


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Bradley Efron. Carl Morris. "Multivariate Empirical Bayes and Estimation of Covariance Matrices." Ann. Statist. 4 (1) 22 - 32, January, 1976.


Published: January, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0322.62041
MathSciNet: MR394960
Digital Object Identifier: 10.1214/aos/1176343345

Primary: 62F10
Secondary: 62C99

Keywords: combining estimates , estimating a covariance matrix , James-Stein estimator , mean of a multivariate normal distribution , minimax estimation , multivariate empirical Bayes , simultaneous estimation , Stein's estimator

Rights: Copyright © 1976 Institute of Mathematical Statistics


Vol.4 • No. 1 • January, 1976
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