## Empirical Bayes rules for selecting the best normal population compared with a control.(English)Zbl 0804.62009

Summary: The problem of selecting the population with the largest mean from among $$k$$ $$(\geq 2)$$ independent normal populations is investigated. The population to be selected must be as good as or better than a control. It is assumed that past observations are available when the current selection is made. Accordingly, the empirical Bayes approach is employed. Combining useful information from the past data, empirical Bayes selection procedures are developed. It is proved that the proposed empirical Bayes selection procedures are asymptotically optimal, having a rate of convergence of order $$O((\ln n)^ 2/n)$$, where $$n$$ is the number of past observations at hand. A simulation study is also carried out to investigate the performance of the proposed empirical Bayes selection procedures for small to moderate values of $$n$$.

### MSC:

 62C12 Empirical decision procedures; empirical Bayes procedures 62F07 Statistical ranking and selection procedures