CONTROL-VARIATE MODELS OF COMMON RANDOM NUMBERS FOR MULTIPLE COMPARISONS WITH THE BEST

Using common random numbers (CRN) in simulation experiment design is k nown to reduce the variance of estimators of differences in system per formance. However, when more than two systems are compared, exact simu ltaneous statistical inference in conjunction with CRN is typically im possible. We introduce control-variate models of CRN that permit exact statistical inference, specifically multiple comparison's with the be st. These models explain the effect of CRN via a linear regression of the simulation output on ''control variates'' that are functions of th e simulation inputs. We establish theoretically, and illustrate empiri cally, that the control-variate models lead to sharper statistical inf erence in the sense that the probability of detecting differences in s ystems' performance is increased.