Replicated Batch Means Variance Estimators in the Presence of an Initial Transient

Independent replications (IR) and batch means (BM) are two of the most widely used variance-estimation methods for simulation output analysis. Andradóttir and Argon (2002) proposed the method of replicated batch means (RBM), which combines good characteristics of IR and BM. The current paper gives analytical results for the mean and variance of the RBM estimator for a class of processes having an initial transient with an additive form. Along the way, we provide complementary extensions of the main variance result in the Andradóttir and Argon paper. An example illustrates our findings