Selecting the most reliable Poisson population provided it is better than a control: a nonparametric empirical Bayes approach

Abstract

We study the problem of selecting the most reliable Poisson population from among k competitors provided it is better than a control using the nonparametric empirical Bayes approach. An empirical Bayes selection procedure is constructed based on the isotonic regression estimators of the posterior means of failure rates associated with the k Poisson populations. The asymptotic optimality of the empirical Bayes selection procedure is investigated. Under certain regularity conditions, we have shown that the proposed empirical Bayes selection procedure is asymptotically optimal and the associated Bayes risk converges to the minimum Bayes risk at a rate of order O(exp(− cn)) for some c>0, where n denotes the number of historical data at hand when the present selection problem is considered.