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Biometrika 1971 58(1):244; doi:10.1093/biomet/58.1.244
© 1971 by Biometrika Trust
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MISCELLANEA

Evaluation of empirical Bayes estimators for small numbers of past samples

STEPHEN L. GEORGE

The University of Texas M. D. Anderson Hospital and Tumor Institute Houston, Texas

The usual technique for evaluating the performance of empirical Bayes estimators for small numbers, N, of past observations is to compare by Monte Carlo techniques the global risk for the empirical Bayes estimator to the risk obtained for some optimal non-Bayes estimator {delta}. Here it is shown, under fairly general conditions, that if the prior variance ß2 is small relative to the Bayes risk of {delta}, and if N!= 0, then one can always find an estimator that is better than {delta}, regardless of the form of the prior G or the magnitude of N.

Key Words: Empirical Bayes estimation • Comparison of empirical Bayes and other estimates


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