Evaluation of empirical Bayes estimators for small numbers of past samples

Abstract

SUMMARY 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 δ. Here it is shown, under fairly general conditions, that if the prior variance β2 is small relative to the Bayes risk of δ, and if N ≠ 0, then one can always find an estimator that is better than δ, regardless of the form of the prior G or the magnitude of N .