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Exact expected values of variance estimators for simulation

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  • Tûba Aktaran‐Kalaycı
  • Christos Alexopoulos
  • Nilay Tanık Argon
  • David Goldsman
  • James R. Wilson

Abstract

We formulate exact expressions for the expected values of selected estimators of the variance parameter (that is, the sum of covariances at all lags) of a steady‐state simulation output process. Given in terms of the autocovariance function of the process, these expressions are derived for variance estimators based on the simulation analysis methods of nonoverlapping batch means, overlapping batch means, and standardized time series. Comparing estimator performance in a first‐order autoregressive process and the M/M/1 queue‐waiting‐time process, we find that certain standardized time series estimators outperform their competitors as the sample size becomes large. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Suggested Citation

  • Tûba Aktaran‐Kalaycı & Christos Alexopoulos & Nilay Tanık Argon & David Goldsman & James R. Wilson, 2007. "Exact expected values of variance estimators for simulation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 397-410, June.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:4:p:397-410
    DOI: 10.1002/nav.20215
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    References listed on IDEAS

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    1. Wheyming Tina Song & Bruce W. Schmeiser, 1993. "Variance of the Sample Mean: Properties and Graphs of Quadratic-Form Estimators," Operations Research, INFORMS, vol. 41(3), pages 501-517, June.
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    4. David Goldsman & Keebom Kang & Andrew F. Seila, 1999. "Cramér-von Mises Variance Estimators for Simulations," Operations Research, INFORMS, vol. 47(2), pages 299-309, April.
    5. Bruce Schmeiser, 1982. "Batch Size Effects in the Analysis of Simulation Output," Operations Research, INFORMS, vol. 30(3), pages 556-568, June.
    6. Lee Schruben, 1983. "Confidence Interval Estimation Using Standardized Time Series," Operations Research, INFORMS, vol. 31(6), pages 1090-1108, December.
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    Cited by:

    1. Mingchang Chih, 2019. "An Insight into the Data Structure of the Dynamic Batch Means Algorithm with Binary Tree Code," Mathematics, MDPI, vol. 7(9), pages 1-8, August.
    2. Song, Wheyming Tina, 2019. "The Song rule outperforms optimal-batch-size variance estimators in simulation output analysis," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1072-1082.
    3. Nilay Tanık Argon & Sigrún Andradóttir & Christos Alexopoulos & David Goldsman, 2013. "Steady-State Simulation with Replication-Dependent Initial Transients: Analysis and Examples," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 177-191, February.

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