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Standardized Time Series Lp-Norm Variance Estimators for Simulations

Author

Listed:
  • Gamze Tokol

    (Earley Corporation, Decatur, Georgia 30030)

  • David Goldsman

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205)

  • Daniel H. Ockerman

    (Retek Information Systems, 7 Piedmont Center, Suite 501, Atlanta, Georgia 30305)

  • James J. Swain

    (Department of Industrial and Systems Engineering, University of Alabama in Huntsville, Huntsville, Alabama 35899)

Abstract

This paper studies a class of estimators for the variance parameter of a stationary stochastic process. The estimators are based on L p norms of standardized time series, and they generalize previously studied estimators due to Schruben. We show that the new estimators have some desirable properties: they are asymptotically unbiased and have low asymptotic variance. We also illustrate empirically the performance of the L p -norm estimators on various stochastic processes.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:2:p:234-245
    DOI: 10.1287/mnsc.44.2.234
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    References listed on IDEAS

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    1. 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.
    2. Benjamin Melamed, 1991. "TES: A Class of Methods for Generating Autocorrelated Uniform Variates," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 317-329, November.
    3. Chiahon Chien & David Goldsman & Benjamin Melamed, 1997. "Large-Sample Results for Batch Means," Management Science, INFORMS, vol. 43(9), pages 1288-1295, September.
    4. 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.
    5. 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.
    6. Ward Whitt, 1989. "Planning Queueing Simulations," Management Science, INFORMS, vol. 35(11), pages 1341-1366, November.
    7. Wheyming Tina Song & Bruce W. Schmeiser, 1995. "Optimal Mean-Squared-Error Batch Sizes," Management Science, INFORMS, vol. 41(1), pages 110-123, January.
    8. 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. Ockerman, Daniel H. & Goldsman, David, 1999. "Student t-tests and compound tests to detect transients in simulated time series," European Journal of Operational Research, Elsevier, vol. 116(3), pages 681-691, August.
    2. James M. Calvin & Marvin K. Nakayama, 2006. "Permuted Standardized Time Series for Steady-State Simulations," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 351-368, May.

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