Simultaneously selecting normal populations close to a control

Abstract

We study the problem of selecting populations close to a control from among k normal populations using the parametric empirical Bayes approach. A Bayes selection rule is derived, which depends on certain parameters. When those parameters are unknown, using the empirical Bayes idea, we first present estimators, based on information collected from the k populations for the unknown parameters. Then, mimicking the behavior of the Bayes selection rule, an empirical Bayes selection rule is constructed. The relative regret Bayes risk is used as a measure of performance of the empirical Bayes selection rule. It is shown that the relative regret Bayes risk of the proposed empirical Bayes selection rule converges to zero at a rate of order O( k −1). A simulation study is also carried out to investigate the performance of the proposed empirical Bayes selection rule for small to moderate values of k.