A Batch Means Methodology for Estimation of a Nonlinear Function of a Steady-State Mean
针对仿真输出中无法直接表示为稳态均值的性能测度（如方差、比率、条件期望），提出一种基于批均值的Jackknife方法，以降低点估计偏差并构建渐近有效的置信区间。
We study the estimation of steady-state performance measures from an ℜ d -valued stochastic process Y = {Y(t): t ≥ 0} representing the output of a simulation. In many applications, we may be interested in the estimation of a steady-state performance measure that cannot be expressed as a steady-state mean r, e.g., the variance of the steady-state distribution, the ratio of steady-state means, and steady-state conditional expectations. These examples are particular cases of a more general problem—the estimation of a (nonlinear) function f(r) of r. We propose a batch-means-based methodology that allows us to use jackknifing to reduce the bias of the point estimator. Asymptotically valid confidence intervals for f(r) are obtained by combining three different point estimators (classical, batch means, and jackknife) with two different variability estimators (classical and jackknife). The performances of the point estimators are discussed by considering asymptotic expansions for their biases and mean squared errors. Our results show that, if the run length is large enough, the jackknife point estimator provides the smallest bias, with no significant increase in the mean squared error.