The purpose of this paper is to obtain weaker sufficient conditions than those given by Robbins  for the asymptotic optimality of empirical Bayes procedures. In so doing a general method for providing asymptotic optimality is given which because of its simplicity should prove quite useful not only for the empirical Bayes problem but for other related asymptotic problems as well. Three areas of application are indicated herein.
"Asymptotic Optimality of the Empirical Bayes Procedure." Ann. Statist. 4 (3) 576 - 580, May, 1976. https://doi.org/10.1214/aos/1176343462