ON EMPIRICAL BAYES SIMULTANEOUS SELECTION PROCEDURES FOR COMPARING NORMAL POPULATIONS WITH A STANDARD

In this paper, we derive statistical selection procedures to partition k normal popu-lations into "good " or "bad " ones, respectively, using the nonparametric empirical Bayes approach. The relative regret risk of a selection procedure is used as a measure of its performance. We establish the asymptotic optimality of the proposed empirical Bayes selection procedures and investigate the associated rates of convergence. Under a very mild condition, the proposed empirical Bayes selection procedures are shown to have rates of convergence of order close to 0{k~*) where k is the number of populations involved in the selection problem. With further strong assumptions, the empirical Bayes selection procedures have rates of convergence of order 0(k 2r+l), where 1 < a < 2 and r is an integer greater than 2