Large-Sample Results for Batch Means

Chiahon Chien, David Goldsman and Benjamin Melamed
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Chiahon Chien: Silicon Sorcery, Saratoga, California 95070
David Goldsman: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Benjamin Melamed: Department of Management Science and Information Systems, Faculty of Management, Rutgers University, New Brunswick, New Jersey 08903

Management Science, 1997, vol. 43, issue 9, 1288-1295

Abstract: In analyzing the output process generated by a steady-state simulation, we often seek to estimate the expected value of the output. The sample mean based on a finite sample of size n is usually the estimator of choice for the steady-state mean; and a measure of the sample mean's precision is the variance parameter, i.e., the limiting value of the sample size multiplied by the variance of the sample mean as n becomes large. This paper establishes asymptotic properties of the conventional batch-means (BM) estimator of the variance parameter as both the batch size and the number of batches become large. In particular, we show that the BM variance estimator is asymptotically unbiased and convergent in mean square. We also provide asymptotic expressions for the variance of the BM variance estimator. Exact and empirical examples illustrate our findings.

Keywords: simulation; stationary process; variance estimation; batch means estimator (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:43:y:1997:i:9:p:1288-1295

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