Empirical Bayes Selection for the Highest Probability of Success in Negative Binomial Distributions

摘要

The author studies the problem of selecting the highest probability of success from among several negative binomial distributions via the nonparametric empirical Bayes approach. A monotone selection rule is proposed on basis of monotone empirical Bayes estimators of the negative binomial success probabilities which are obtained by using the antitonic and isotonic regression methods. The asymptotic optimality property of the proposed empirical Bayes selection rule is also established. (KR)