Consider k(k~2) populations whose meanei and variance a} are all unknown. For
given control values θand σ²'";, we are interested in selecting some population whose
mean is the largest in the qualified subset in which each mean is larger than or equal toθ
and whose variance is less than or equal to σ²; . In this paper we focus on the case of
normal populations. However, the analogous method can be applied for the cases other
than normal. A Bayes approach is set up and an empirical Bayes procedure is proposed
which has been shown to be asymptotically optimal.
