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.
"An Adaptive Solution to Ranking and Selection Problems." Ann. Statist. 6 (3) 658 - 672, May, 1978. https://doi.org/10.1214/aos/1176344210