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Variance reduction for quantile estimates in simulations via nonlinear controls

 

作者: Richard L. Ressler,   Peter A. W. Lewis,  

 

期刊: Communications in Statistics - Simulation and Computation  (Taylor Available online 1990)
卷期: Volume 19, issue 3  

页码: 1045-1077

 

ISSN:0361-0918

 

年代: 1990

 

DOI:10.1080/03610919008812905

 

出版商: Marcel Dekker, Inc.

 

关键词: variance reduction;quantiles;nonlinear controls;trans-formations;ACE;least-squares regression;jackknifing

 

数据来源: Taylor

 

摘要:

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 relation-ship 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 obtain 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

 

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