Regression-Based Methods for Using Control Variates in Monte Carlo Experiments

Methods based on linear regression provide an easy way to use the information in control variates to improve the efficiency with which certain features of the distributions of estimators and test statistics are estimated in Monte Carlo experiments. We propose a new technique that allows these methods to be used when the quantities of interest are quantiles. We also propose new ways to obtain approximately optimal control variates in many cases of interest. These methods seem to work well in practice, and can greatly reduce the number of replications required to obtain a given level of accuracy.