Replicated batch means for steady-state simulations with initial transients

Authors:
Christos Alexopoulos;Sigrún Andradóttir;Nilay Tanik Argon;David Goldsman
Affiliations:
Georgia Institute of Technology, Atlanta, GA;Georgia Institute of Technology, Atlanta, GA;University of North Carolina, Chapel Hill, NC;Georgia Institute of Technology, Atlanta, GA
Venue:
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Year:
2007

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Abstract

We provide asymptotic expressions for the expected value and variance of the replicated batch means variance estimator when the stochastic process being simulated has an additive initial transient. These expressions explicitly show how the initial transient and the autocorrelation in the data affect the performance of the estimator. We apply our results to study how many replications will minimize the asymptotic bias of the variance estimator for a simple example.