ε asymptotic optimality of empirical Bayes estimators

Abstract

Robbins (1964) gives conditions under which empirical Beyes estimators are asymptotically optimal. The conditions require the loss function to be bounded in the parameter. This does not hold in some important situations including the squared error loss. Here we give weaker conditions and prove a weaker result, ε asymptotic optimality, which is equivalent to asymptotic optimality in practical situations.