Large-Sample Results for Batch Means
研究稳态仿真中批次均值方差估计量的渐近性质，证明其无偏性和均方收敛性，并给出方差表达式，对从事仿真实验的经济学者有参考价值。
In analyzing the output process generated by a steady-state simulation, we often seek to estimate the expected value of the output. The sample mean based on a finite sample of size n is usually the estimator of choice for the steady-state mean; and a measure of the sample mean's precision is the variance parameter, i.e., the limiting value of the sample size multiplied by the variance of the sample mean as n becomes large. This paper establishes asymptotic properties of the conventional batch-means (BM) estimator of the variance parameter as both the batch size and the number of batches become large. In particular, we show that the BM variance estimator is asymptotically unbiased and convergent in mean square. We also provide asymptotic expressions for the variance of the BM variance estimator. Exact and empirical examples illustrate our findings.