Subset selection of superior populations when the number of populations is large (Q1067712)

The situation where k populations are partitioned into one inferior group and one superior group is considered. The statistical problem is to select a random size subset of superior populations while trying to avoid including any inferior populations. A selection procedure is assumed to satisfy the condition that the probability of selecting at least one superior population is bounded below by \(P^*<1\). The performance of a procedure is measured by the probability of including an inferior population. The asymptotic performance, as \(k\to \infty\), of Gupta's traditional maximum type procedure \(\psi^ G\) is considered in the location-model. For normally distributed populations, \(\psi^ G\) turns out to be asymptotically optimal, provided the size of the inferior group does not become infinitely larger than the size of the superior group.