Variance estimation using replicated batch means

Abstract

We present a new method for obtaining confidence intervals in steady-state simulation. In our replicated batch means method, we perform a small number of independent replications to estimate the steady-state mean of the underlying stochastic process. In order to obtain a variance estimator, we further group the observations from these replications into nonoverlapping batches. We show that for large sample sizes, the new variance estimator is less biased than the batch means variance estimator, the variances of the two variance estimators are approximately equal, and the new steady-state mean estimator has a smaller variance than the batch means estimator when there is positive serial correlation between the observations. For small sample sizes, we compare our replicated batch means method with the (standard) batch means and multiple replications methods empirically, and show that the best overall coverage of confidence intervals is obtained by the replicated batch means method with a small number of replications.