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Combining standardized time series area and Cramér–von Mises variance estimators

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  • David Goldsman
  • Keebom Kang
  • Seong‐Hee Kim
  • Andrew F. Seila
  • Gamze Tokol

Abstract

We propose three related estimators for the variance parameter arising from a steady‐state simulation process. All are based on combinations of standardized‐time‐series area and Cramér–von Mises (CvM) estimators. The first is a straightforward linear combination of the area and CvM estimators; the second resembles a Durbin–Watson statistic; and the third is related to a jackknifed version of the first. The main derivations yield analytical expressions for the bias and variance of the new estimators. These results show that the new estimators often perform better than the pure area, pure CvM, and benchmark nonoverlapping and overlapping batch means estimators, especially in terms of variance and mean squared error. We also give exact and Monte Carlo examples illustrating our findings.© 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:4:p:384-396
    DOI: 10.1002/nav.20214
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. David Goldsman & Lee Schruben, 1990. "Note---New Confidence Interval Estimators Using Standardized Time Series," Management Science, INFORMS, vol. 36(3), pages 393-397, March.
    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. 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.

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