An investigation of nonlinear controls and regression-adjusted estimators for variance reduction in computer simulation.

Abstract

This dissertation develops new techniques for variance reduction in computer simulation. It demonstrates that applying nonlinear transformations to control variables can increase their effectiveness over linear controls. It shows how one can reduce the variance of quantile estimates, where the quantile of interest is a continuous and strictly monotone transformation of the control quantile, by transforming the control quantile with a different continuous and strictly monotone transformation. Asymptotic expansions are developed to validate the improved performance of the nonlinear control for the quantile estimate. Finally, in the realm of regenerative simulation, regression-adjusted techniques are applied to controlled regenerative estimates. The resulting estimates have a greatly reduced estimated mean square error.