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Cramér-von Mises Variance Estimators for Simulations

Author

Listed:
  • David Goldsman

    (Georgia Institute of Technology, Atlanta, Georgia)

  • Keebom Kang

    (Naval Postgraduate School, Monterey, California)

  • Andrew F. Seila

    (University of Georgia, Athens, Georgia)

Abstract

We study estimators for the variance parameter σ 2 of a stationary process. The estimators are based on weighted Cramér-von Mises statistics, and certain weightings yield estimators that are “first-order unbiased” for σ 2 . We derive an expression for the asymptotic variance of the new estimators; this expression is then used to obtain the first-order unbiased estimator having the smallest variance among fixed-degree polynomial weighting functions. Our work is based on asymptotic theory; however, we present exact and empirical examples to demonstrate the new estimators' small-sample robustness. We use a single batch of observations to derive the estimators' asymptotic properties, and then we compare the new estimators among one another. In real-life applications, one would use more than one batch; we indicate how this generalization can be carried out.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:2:p:299-309
    DOI: 10.1287/opre.47.2.299
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    References listed on IDEAS

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    1. Robert S. Sargent & Keebom Kang & David Goldsman, 1992. "An Investigation of Finite-Sample Behavior of Confidence Interval Estimators," Operations Research, INFORMS, vol. 40(5), pages 898-913, October.
    2. Peter W. Glynn & Donald L. Iglehart, 1990. "Simulation Output Analysis Using Standardized Time Series," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 1-16, February.
    3. David Goldsman & Marc Meketon & Lee Schruben, 1990. "Properties of Standardized Time Series Weighted Area Variance Estimators," Management Science, INFORMS, vol. 36(5), pages 602-612, May.
    4. Ward Whitt, 1989. "Planning Queueing Simulations," Management Science, INFORMS, vol. 35(11), pages 1341-1366, November.
    5. David Goldsman & Lee Schruben, 1990. "Note---New Confidence Interval Estimators Using Standardized Time Series," Management Science, INFORMS, vol. 36(3), pages 393-397, March.
    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. 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.
    2. David Goldsman & Keebom Kang & Seong‐Hee Kim & Andrew F. Seila & Gamze Tokol, 2007. "Combining standardized time series area and Cramér–von Mises variance estimators," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 384-396, June.
    3. Christos Alexopoulos & David Goldsman & Gamze Tokol, 2001. "Properties of Batched Quadratic-Form Variance Parameter Estimators for Simulations," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 149-156, May.

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