Control variates for screening, selection, and estimation of the best

Abstract

Ranking and selection procedures (R&S) were developed by statisticians to search for the best among a small collection of populations or treatments, where the “best” treatment is typically the one with the largest or smallest expected(long-run average) response. R&S procedures have been successfully extended to address situations that are encountered in stochastic simulation of alternative system designs, including unequal variances across alternatives, dependence both within the output of each system and across the outputs from alternative systems, and large numbers of alternatives to compare. In nearly all cases the estimator of the expected response is a (perhaps generalized) sample mean of the output of interest. In this article we derive R&S procedures that employ control-variate estimators instead of sample means. Control variates can be much more statistically efficient than sample means, leading to R&S procedures that are correspondingly more efficient. We also consider the related problem of estimating the expected value of the best (as opposed to the selected) system design.