Combining antithetic variates and control variates in simulation experiments

Abstract

Antithetic variates and control variates are two well-known variance reduction techniques. We consider combining antithetic variates and control variates to estimate the mean response in a stochastic simulation experiment. When applying antithetic variates to generate control variates across paired replications, we show that the integrated control-variate estimator is unbiased and yields, under the assumption of common correlations induced for all control variates, a smaller variance than the conventional control-variate estimator without using antithetic variates. We examine the proposed estimator and two alternative integrated control-variate estimators when applying antithetic variates on control variates and show that the proposed estimator is the optimal integrated control-variate estimator We implement these three integrated control-variate estimators and the conventional control-variate estimator in a simulation model of a stochastic network to evaluate the performance of each control-variate estimator Empirical results show that the proposed estimator outperforms the other control-variate estimators.