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Properties of Standardized Time Series Weighted Area Variance Estimators

Author

Listed:
  • David Goldsman

    (School of ISyE, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Marc Meketon

    (AT&T Bell Laboratories, Holmdel, New Jersey 07733)

  • Lee Schruben

    (School of OR&IE, Cornell University, Ithaca, New York 14853)

Abstract

We wish to estimate the variance of the sample mean from a continuous-time stationary stochastic process. This article expands on the results of a technical note (Goldsman and Schruben 1990) by using the theory of standardized time series to investigate weighted generalizations of Schruben's area variance estimator. We find a simple expression for the bias of the weighted area variance estimator, and we give weights which yield variance estimators with lower asymptotic bias than certain other popular estimators. We use the weighted area variance estimators to derive asymptotically valid confidence interval estimators (CIEs) for the mean of a stationary stochastic process. Although the weighted area CIEs have the same asymptotic expected value and variance of the length as Schruben's area CIE, we show that the new CIEs sometimes yield coverages which are closer to the nominal value.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:5:p:602-612
    DOI: 10.1287/mnsc.36.5.602
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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. 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.
    3. Barry L. Nelson, 2004. "50th Anniversary Article: Stochastic Simulation Research in Management Science," Management Science, INFORMS, vol. 50(7), pages 855-868, July.
    4. 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.
    5. 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.
    6. Christos Alexopoulos & Nilay Tanık Argon & David Goldsman & Natalie M. Steiger & Gamze Tokol & James R. Wilson, 2007. "Efficient Computation of Overlapping Variance Estimators for Simulation," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 314-327, August.
    7. 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.
    8. 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.
    9. 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.

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