On a Class of Subset Selection Procedures

Abstract

A class of procedures is considered for the subset selection problem when the populations are from a stochastically increasing family $\{F_\lambda\}$. A theorem concerning the monotonicity of an integral associated with $\{F_\lambda\}$ which generalizes an earlier result of Lehmann is obtained. This leads to a sufficient condition for the monotonicity of the probability of a correct selection for the procedure considered. It is shown that this condition is relevant to another sufficient condition for the supremum of the expected subset size to occur when the distributions are identical. The main results are applied to the specific cases where (i) $\lambda$ is a location parameter (ii) $\lambda$ is a scale parameter and (iii) the case where the density $f_\lambda(x)$ is a convex mixture of a sequence of known density functions. The earlier known results are shown to follow from the general theory.