方差缩减中的控制变量方法研究

Research on Control-variate Estimators of Variance Reduction

方差缩减方法是提高仿真效率的重要手段。针对方差缩减中广泛应用的控制变量法,在国内外研究基础上,综合考虑对仿真变量进行估计所需的样本量和对控制变量进行估计所需的样本量,给出了控制变量均值未知并且有偏时的估计,以及控制变量方差已知时依赖于样本量和样本协方差的复合估计。引入控制变量的计算效率比,综合考虑各种估计方法的方差及其仿真样本量。

Variance Reduction （VR） is an important way to raise simulation estimation efficiency, and Control Variate （CV） estimators are widely used for variance reduction. Based on much works in developing and analyzing CV estimators＇, some further researches are given. Control variate estimation is studied where the control mean itself is unbiased estimated, and take both prior and auxiliary simulation replications into consideration. Analyzing control variate estimator is focus on where the control variance is known, and given a compound estimator depending on simulation replications and covariances. Then the efficiency combining control variate variances and replication costs are consided.