Variance Reduction Of Quantile Estimates Via Nonlinear Controls

Linear Controls are a well known technique for achieving variance reduction in computer simulation. Unfortunately the effectiveness of a linear control depends upon the correlation between the statistic of interest and the control which is often low. Since statistics are often nonlinear functions of the control this implies that nonlinear controls offer a means for improvement over linear controls. Nonlinear controls have had succes over linear controls. Nonlinear controls have had success in increasing the variance reduction over a linear control. This current work focuses on the use of nonlinear controls for reducing the variance of quantile estimates. The paper begins with a short discussion of linear controls. It describes nonlinear controls and the possibility for improved performance. The final sections discuss quantiles as controls and the potential of nonlinear controls for variance reduction in quantile estimation.