IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v44y1998i2p234-245.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.44.2.234
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.44.2.234?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
    ---><---

    References listed on IDEAS

    as
    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.
    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. 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.

    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. 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.
    2. 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.
    3. 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.
    4. Seong-Hee Kim & Barry L. Nelson, 2006. "On the Asymptotic Validity of Fully Sequential Selection Procedures for Steady-State Simulation," Operations Research, INFORMS, vol. 54(3), pages 475-488, June.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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. 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.
    12. 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.
    13. Halkos, George & Kevork, Ilias, 2002. "Confidence intervals in stationary autocorrelated time series," MPRA Paper 31840, University Library of Munich, Germany.
    14. Sheth-Voss, Pieter A. & Willemain, Thomas R. & Haddock, Jorge, 2005. "Estimating the steady-state mean from short transient simulations," European Journal of Operational Research, Elsevier, vol. 162(2), pages 403-417, April.
    15. Halim Damerdji & David Goldsman, 1995. "Consistency of several variants of the standardized time series area variance estimator," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1161-1176, December.
    16. 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.
    17. Halkos, George & Kevork, Ilias, 2006. "Estimating population means in covariance stationary process," MPRA Paper 31843, University Library of Munich, Germany.
    18. Natalie M. Steiger & James R. Wilson, 2001. "Convergence Properties of the Batch Means Method for Simulation Output Analysis," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 277-293, November.
    19. 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.
    20. Feng Yang & Bruce E. Ankenman & Barry L. Nelson, 2008. "Estimating Cycle Time Percentile Curves for Manufacturing Systems via Simulation," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 628-643, November.

    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:inm:ormnsc:v:44:y:1998:i:2:p:234-245. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.