An Adaptive Solution to Ranking and Selection Problems

Abstract

An adaptive approach is considered as an alternative to the classical indifference-zone formulation of the problems of ranking and selection. With a fixed $\gamma^\ast$, the proposed procedure calls for the termination of sampling when the estimated probability of correct selection exceeds $\gamma^\ast$ for the first time. Asymptotic properties of this procedure are proved as $\gamma^\ast \rightarrow 1$, and Monte Carlo results show that the procedure is well behaved even for moderate $\gamma^\ast$. Since the stopping variables depend on the estimators of the ordered parameters, distributions of the estimators as functions of the parameters are carefully studied via majorization.