Replicated batch means variance estimators in the presence of an initial transient

Abstract

Independent replications (IR) and batch means (BM) are two of the most widely used variance-estimation methods for simulation output analysis. Alexopoulos and Goldsman conducted a thorough examination of IR and BM; and Andradóttir and Argon proposed the method of replicated batch means (RBM), which combines good characteristics of IR and BM. This article gives analy-tical results for the mean and variance of the RBM estimator for a class of processes having initial transients with an additive form. Along the way, we provide succinct complementary extensions of some of the results in the aforementioned papers. Our expressions explicitly show how the transient function affects estimator performance and suggest that in some cases, the RBM estimator is a good compromise choice with respect to bias and variance. However, care must be taken to avoid an excessive number of replications when the transient function is pervasive. An example involving a simple moving average process illustrates our findings.