On improving standard estimators via linear empirical Bayes methods

Suppose one wishes to estimate the parameter theta in a current experiment when one also has in hand data from k past experiments satisfying empirical Bayes sampling assumptions. It has long been known that, for a variety of models, empirical Bayes estimators tend to outperform, asymptotically, standard estimators based on the current experiment alone. Much less is known about the superiority of empirical Bayes estimators over standard estimators when k is fixed; what is known in that regard is largely the product of Monte Carlo studies. Conditions are given here under which certain linear empirical Bayes estimators are superior to the standard estimator for arbitrary k greater than or equal to 1. (C) 1999 Elsevier Science B.V. All rights reserved.