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Mean-Square Consistency of the Variance Estimator in Steady-State Simulation Output Analysis

Author

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  • Halim Damerdji

    (North Carolina State University, Raleigh, North Carolina)

Abstract

In steady-state simulation output analysis, mean-square consistency of the process-variance estimator is important for a number of reasons. One way to construct an asymptotically valid confidence interval around a sample mean is via construction of a consistent estimator of the process variance and a central limit theorem. Also, if an estimator is consistent in the mean-square sense, a mean-square error analysis is theoretically justified. Finally, batch-size selection is an open research problem in steady-state output analysis, and a mean-square error analysis approach has been proposed in the literature; to be valid, the process-variance estimators constructed must be consistent in the mean-square sense. In this paper, we prove mean-square consistency of the process-variance estimator for the methods of batch means, overlapping batch means, standardized time series (area), and spaced batch means, by rigorously computing the rate of decay of the variance of the process-variance estimators. Asymptotic results for third and higher centered moments of the batch means and area variance estimators are also given, along with central limit theorems.

Suggested Citation

  • Halim Damerdji, 1995. "Mean-Square Consistency of the Variance Estimator in Steady-State Simulation Output Analysis," Operations Research, INFORMS, vol. 43(2), pages 282-291, April.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:2:p:282-291
    DOI: 10.1287/opre.43.2.282
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    Citations

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    Cited by:

    1. David Goldsman & Seong-Hee Kim & William S. Marshall & Barry L. Nelson, 2002. "Ranking and Selection for Steady-State Simulation: Procedures and Perspectives," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 2-19, February.
    2. Seong-Hee Kim & Barry L. Nelson, 2006. "On the Asymptotic Validity of Fully Sequential Selection Procedures for Steady-State Simulation," Operations Research, INFORMS, vol. 54(3), pages 475-488, June.
    3. Meterelliyoz, Melike & Alexopoulos, Christos & Goldsman, David, 2012. "Folded overlapping variance estimators for simulation," European Journal of Operational Research, Elsevier, vol. 220(1), pages 135-146.
    4. Gamze Tokol & David Goldsman & Daniel H. Ockerman & James J. Swain, 1998. "Standardized Time Series Lp-Norm Variance Estimators for Simulations," Management Science, INFORMS, vol. 44(2), pages 234-245, February.
    5. Christos Alexopoulos & Nilay Tanık Argon & David Goldsman & Gamze Tokol & James R. Wilson, 2007. "Overlapping Variance Estimators for Simulation," Operations Research, INFORMS, vol. 55(6), pages 1090-1103, December.
    6. Ying Liu & Dootika Vats & James M. Flegal, 2022. "Batch Size Selection for Variance Estimators in MCMC," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 65-93, March.
    7. David F. Muñoz & Peter W. Glynn, 2001. "Multivariate Standardized Time Series for Steady-State Simulation Output Analysis," Operations Research, INFORMS, vol. 49(3), pages 413-422, June.
    8. Kin Wai Chan & Chun Yip Yau, 2017. "High-order Corrected Estimator of Asymptotic Variance with Optimal Bandwidth," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 866-898, December.

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