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Variance reduction for quantile estimates in simulations via nonlinear controls

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Author
Lewis, Peter A. W.
Ressler, Richard L.
Date
1990-04
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Abstract
Linear controls are a well known simple 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 often have a nonlinear relationship with the potential control variables, nonlinear controls offer a means for improvement over linear controls. This paper focuses on the use of nonlinear controls for reducing the variance of quantile estimates in simulation. It is shown that one can substantially reduce the analytic effort required to develop a nonlinear control from a quantile estimator by using a strictly monotone transformation to create the nonlinear control. It is also shown that as one increases the sample size for the quantile estimator, the asymptotic multivariate normal distribution of the quantile of interest and the control reduces the effectiveness of the nonlinear control to that of the linear control. However, the data has to be sectioned to obtained an estimate of the variance of the controlled quantile estimate. Graphical methods are suggested for selecting the section size that maximizes the effectiveness of the nonlinear control. Keyword: Variance reduction, Quantiles; Nonlinear controls; Transformation; ACE; Least-squares regression; Jackknifing. (kr)
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
URI
http://hdl.handle.net/10945/30279
NPS Report Number
NPS-55-90-09
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  • Thumbnail

    Variance Reduction of Quantile Estimates via Nonlinear Controls 

    Lewis, Peter A.W.; Ressler, Richard L. (1989);
    Linear controls are a well known techniques for achieving variance reduction in computer simulation. Unfortunately the effectiveness of a linear control depends upon the correlation between the statistic of interest and ...
  • Thumbnail

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

    Ressler, Richard L. (Monterey, California. Naval Postgraduate School, 1991-03);
    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. ...
  • Thumbnail

    Variance Reduction using Nonlinear Control and Transformations 

    Lewis, Peter A.W.; Ressler, Richard L.; Wood, R. Kevin (Monterey, California: Naval Postgraduate School., 1988-08); NPS55-88-007
    Nonlinear regression-adjusted control variables are investigated for improving variance reduction in statistical and systems simulations. To this end, simple control variables are piecewise sectioned and then transformed ...
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