Variance Reduction Using Nonlinear Controls and Transformations

Abstract

Nonlinear regression-adjusted control variables are investigated for improving variance reduction in statistical and system simulations. To this end, simple control variables are piecewise sectioned and then transformed using linear and nonlinear transformations. Optimal parameters of these transformations are selected using linear or nonlinear least-squares regression algorithms. As an example, piecewise power-transformed variables are used in the estimation of the mean for the twovariable Anderson-Darling goodness-of-fit statistic W ₂ ². Substantial variance reduction over straightforward controls is obtained. These parametric transformations are compared against optimal, additive nonparametric transformations obtained by using the ACE algorithm and are shown, in comparison to the results from ACE, to be nearly optimal.

Keywords:

• variance reduction
• nonlinear controls
• transformations
• ACE
• least-squares regression
• correlation