MEAN-SQUARE CONSISTENCY OF THE VARIANCE ESTIMATOR IN STEADY-STATE SIMULATION OUTPUT ANALYSIS

In steady-state simulation output analysis, mean-square consistency of the process-variance estimator is important for a number of reasons. One way to construct an asymptotically valid confidence interval aroun d a sample mean is via construction of a consistent estimator of the p rocess variance and a central limit theorem. Also, if an estimator is consistent in the mean-square sense, a mean-square error analysis is t heoretically justified. Finally, batch-size selection is an open resea rch problem in steady-state output analysis, and a mean-square error a nalysis approach has been proposed in the literature; to be valid, the process-variance estimators constructed must be consistent in the mea n-square sense. In this paper, we prove mean-square consistency of the process-variance estimator for the methods of batch means, overlappin g batch means, standardized time series (area), and spaced batch means , by rigorously computing the rate of decay of the variance of the pro cess-variance estimators. Asymptotic results for third and higher cent ered moments of the batch means and area variance estimators are also given, along with central limit theorems.