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Extended dynamic partial-overlapping batch means estimators for steady-state simulations

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  • Song, Wheyming T.
  • Chih, Mingchang

Abstract

Estimating the variance of the sample mean from a stochastic process is essential in assessing the quality of using the sample mean to estimate the population mean, which is the fundamental question in simulation experiments. Most existing studies for estimating the variance of the sample mean from simulation output assume that the simulation run length is known in advance. An interesting and open question is how to estimate the variance of the sample mean with limited memory space, reasonable computation time, and good statistical properties such as small mean-squared-error (mse), without knowing the simulation run length a priori. This paper proposes a finite-memory algorithm that satisfies the above good estimation criteria. Our findings show that the proposed algorithm improves over its competitors in terms of the mse criterion.

Suggested Citation

  • Song, Wheyming T. & Chih, Mingchang, 2010. "Extended dynamic partial-overlapping batch means estimators for steady-state simulations," European Journal of Operational Research, Elsevier, vol. 203(3), pages 640-651, June.
    • Handle: RePEc:eee:ejores:v:203:y:2010:i:3:p:640-651
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    References listed on IDEAS

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    1. Song, Wheyming Tina, 1996. "On the estimation of optimal batch sizes in the analysis of simulation output," European Journal of Operational Research, Elsevier, vol. 88(2), pages 304-319, January.
    2. R. W. Conway, 1963. "Some Tactical Problems in Digital Simulation," Management Science, INFORMS, vol. 10(1), pages 47-61, October.
    3. 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.
    4. George S. Fishman, 1978. "Grouping Observations in Digital Simulation," Management Science, INFORMS, vol. 24(5), pages 510-521, January.
    5. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    6. Michael A. Crane & Donald L. Iglehart, 1975. "Simulating Stable Stochastic Systems: III. Regenerative Processes and Discrete-Event Simulations," Operations Research, INFORMS, vol. 23(1), pages 33-45, February.
    7. Wheyming T. Song & Bruce W. Schmeiser, 2009. "Omitting Meaningless Digits in Point Estimates: The Probability Guarantee of Leading-Digit Rules," Operations Research, INFORMS, vol. 57(1), pages 109-117, February.
    8. Averill M. Law & John S. Carson, 1979. "A Sequential Procedure for Determining the Length of a Steady-State Simulation," Operations Research, INFORMS, vol. 27(5), pages 1011-1025, October.
    9. Wheyming Tina Song & Bruce W. Schmeiser, 1995. "Optimal Mean-Squared-Error Batch Sizes," Management Science, INFORMS, vol. 41(1), pages 110-123, January.
    10. George S. Fishman & L. Stephen Yarberry, 1997. "An Implementation of the Batch Means Method," INFORMS Journal on Computing, INFORMS, vol. 9(3), pages 296-310, August.
    11. Bruce Schmeiser, 1982. "Batch Size Effects in the Analysis of Simulation Output," Operations Research, INFORMS, vol. 30(3), pages 556-568, June.
    12. 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 & Chih, Mingchang, 2013. "Run length not required: Optimal-mse dynamic batch means estimators for steady-state simulations," European Journal of Operational Research, Elsevier, vol. 229(1), pages 114-123.

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