Consider a stationary stochastic process, X1,X2,..., arising from a steady-state simulation. An important problem is that of estimating the expected value μ of the process. The usual estimator for μ is the sample mean based on n observations, &Xmacr;n, and a measure of the precision of &Xmacr;n is the variance parameter, σ2=limn→∞n Var[&Xmacr;n]. This paper studies asymptotic properties of the batch-means estimator &Vcirc;B(b,m) for σ2 as both the batch size m and number of batches b become large. In particular, we give conditions for &Vcirc;B(b,m) to converge to normality as m and b increase. Empirical examples illustrate our findings.
