Asymptotic results for batch-variance methods in simulation output analysis

We consider the batching methods for estimating the variance of the sample variance based on steady-state correlated data. Intensive research has been devoted to the problem of estimating the variance of the sample mean, but little to the sample variance when the desired performance measure is the population variance. The batch-variance estimator (for the variance of the sample variance) is a function of the batch variances, which are the sample variances of the batched data. By viewing the sample variance as a sample mean of squared terms, we show that the asymptotic results for the batch-variance and batch-mean estimators are analogous in two ways. First, both have the same convergence rates. Second, whether batch means or batch variances are employed, a single rule applies to both multipliers in the asymptotic formula. The constant multipliers are the same, and the other multipliers depend on the data properties, which are analogous for batch variances and batch means with squared terms. We prove these results analytically for the nonoverlapping batch-variance method and argue that they can be extended to cover the overlapping batch-variance method.