A frequentist selection-of-the-best procedure without indifference zone

Many procedures have been proposed in the literature to select the best from a finite set of alternatives. Among these procedures, frequentist procedures are typically designed under an indifference-zone (IZ) formulation, where an IZ parameter needs to be specified by users at the beginning of procedures. The IZ parameter is the smallest difference in the performance measure that the users care. In practice, however, the IZ parameter is often difficult to specify appropriately and may be specified in a conservative way (thus leading to excessive sampling effort). In this paper, we propose a frequentist IZ-free selection-of-the-best procedure. The procedure guarantees to select the best with at least a pre-specified probability of correct selection in an asymptotic regime. Through numerical studies, we show our procedure may out-perform IZ procedures, in terms of total sample size, when the IZ parameter is set conservatively or there are a large number of alternatives.