In the empirical Bayes approach to multiple decision problems, we obtain theorems and lemmas which can be used to obtain asymptotic optimality and rate results in any multiple decision empirical Bayes problem. Applications of these results to a classification problem, a monotone multiple decision, and a selection problem are given. In addition, a special lemma unique to the monotone multiple decision problem gives improved (exact) rate results in that case.
"On the Empirical Bayes Approach to Multiple Decision Problems." Ann. Statist. 5 (1) 172 - 181, January, 1977. https://doi.org/10.1214/aos/1176343750