Adaptive sequential selection procedures for optimal quantile with control variates

This paper introduces adaptive sequential selection procedures leveraging control variate quantile estimators for efficient quantile-based ranking and selection in simulation studies. Two variations are proposed: one simplifies estimation using binary control variates, and the other employs a discrete approximation to derive a post-stratified control variate quantile estimator. Theoretical analysis establishes the asymptotic validity and efficiency of these methods, including a novel central limit theorem for the post-stratified estimator. Numerical experiments on normal distributions and a basic queueing problem demonstrate the superior performance and adaptability of the proposed procedures. This work advances the integration of variance reduction techniques into quantile-based ranking-and-selection procedures, providing a robust framework for practical applications.