IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v229y2013i1p114-123.html
   My bibliography  Save this article

Run length not required: Optimal-mse dynamic batch means estimators for steady-state simulations

Author

Listed:
  • Song, Wheyming Tina
  • Chih, Mingchang

Abstract

This paper addresses the estimation of the variance of the sample mean from steady-state simulations without requiring the knowledge of simulation run length a priori. Dynamic batch means is a new and useful approach to implementing the traditional batch means in limited memory without the knowledge of the simulation run length. However, existing dynamic batch means estimators do not allow one to control the value of batch size, which is the performance parameter of the batch means estimators. In this work, an algorithm is proposed based on two dynamic batch means estimators to dynamically estimate the optimal batch size as the simulation runs. The simulation results show that the proposed algorithm requires reasonable computation time and possesses good statistical properties such as small mean-squared-error (mse).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:1:p:114-123
    DOI: 10.1016/j.ejor.2012.10.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712007655
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.10.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wheyming Tina Song & Bruce W. Schmeiser, 1993. "Variance of the Sample Mean: Properties and Graphs of Quadratic-Form Estimators," Operations Research, INFORMS, vol. 41(3), pages 501-517, June.
    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. George S. Fishman, 1978. "Grouping Observations in Digital Simulation," Management Science, INFORMS, vol. 24(5), pages 510-521, January.
    4. 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.
    5. Wheyming Tina Song & Bruce W. Schmeiser, 1995. "Optimal Mean-Squared-Error Batch Sizes," Management Science, INFORMS, vol. 41(1), pages 110-123, January.
    6. 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.
    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. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    10. 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.
    11. Bruce Schmeiser, 1982. "Batch Size Effects in the Analysis of Simulation Output," Operations Research, INFORMS, vol. 30(3), pages 556-568, June.
    12. 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.
    13. Lee Schruben, 1983. "Confidence Interval Estimation Using Standardized Time Series," Operations Research, INFORMS, vol. 31(6), pages 1090-1108, December.
    14. R. W. Conway, 1963. "Some Tactical Problems in Digital Simulation," Management Science, INFORMS, vol. 10(1), pages 47-61, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    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.
    4. 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.
    5. 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.
    6. 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.
    7. Kin Wai Chan & Chun Yip Yau, 2017. "High-order Corrected Estimator of Asymptotic Variance with Optimal Bandwidth," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 866-898, December.
    8. Halkos, George & Kevork, Ilias, 2002. "Confidence intervals in stationary autocorrelated time series," MPRA Paper 31840, University Library of Munich, Germany.
    9. Natalie M. Steiger & James R. Wilson, 2002. "An Improved Batch Means Procedure for Simulation Output Analysis," Management Science, INFORMS, vol. 48(12), pages 1569-1586, December.
    10. Park, Dae S. & Kim, Yun B. & Shin, Key I. & Willemain, Thomas R., 2001. "Simulation output analysis using the threshold bootstrap," European Journal of Operational Research, Elsevier, vol. 134(1), pages 17-28, October.
    11. Halkos, George & Kevork, Ilias, 2006. "Estimating population means in covariance stationary process," MPRA Paper 31843, University Library of Munich, Germany.
    12. Lada, Emily K. & Wilson, James R., 2006. "A wavelet-based spectral procedure for steady-state simulation analysis," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1769-1801, November.
    13. Enver Yücesan, 1993. "Randomization tests for initialization bias in simulation output," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(5), pages 643-663, August.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. John R. Birge, 2023. "Uses of Sub-sample Estimates to Reduce Errors in Stochastic Optimization Models," Papers 2310.07052, arXiv.org.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:229:y:2013:i:1:p:114-123. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.