Bonferroni-Free and Indifference-Zone-Flexible Sequential Elimination Procedures for Ranking and Selection

This paper proposes two fully sequential procedures for selecting the best system with a guaranteed probability of correct selection (PCS). The main features of the proposed procedures include the following: (1) adopting a Bonferroni-free model that overcomes the conservativeness of the Bonferroni correction and delivers the exact probabilistic guarantee without overshooting; (2) conducting always valid and fully sequential hypothesis tests that enable continuous monitoring of each candidate system and control the type I error rate (or equivalently, PCS) at a prescribed level; and (3) assuming an indifference-zone-flexible formulation, which means that the indifference-zone parameter is not indispensable but could be helpful if provided. We establish statistical validity and asymptotic efficiency for the proposed procedures under normality settings with and without the knowledge of true variances. Numerical studies conducted under various configurations corroborate the theoretical findings and demonstrate the superiority of the proposed procedures.

Funding: W. Wang and H. Wan were supported in part by CollinStar Capital Pty Ltd. X. Chen was supported in part by the National Science Foundation [Grant IIS-1849300 and CAREER CMMI-1846663].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2447.