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An Investigation of Finite-Sample Behavior of Confidence Interval Estimators

Author

Listed:
  • Robert S. Sargent

    (Syracuse University, Syracuse, New York)

  • Keebom Kang

    (Naval Postgraduate School, Monterey, California)

  • David Goldsman

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

We investigate the small-sample behavior and convergence properties of confidence interval estimators (CIEs) for the mean of a stationary discrete process. We consider CIEs arising from nonoverlapping batch means, overlapping batch means, and standardized time series, all of which are commonly used in discrete-event simulation. The performance measures of interest are the coverage probability, and the expected value and variance of the half-length. We use empirical and analytical methods to make detailed comparisons regarding the behavior of the CIEs for a variety of stochastic processes. All the CIEs under study are asymptotically valid; however, they are usually invalid for small sample sizes. We find that for small samples, the bias of the variance parameter estimator figures significantly in CIE coverage performance—the less bias the better. A secondary role is played by the marginal distribution of the stationary process. We also point out that some CIEs require fewer observations before manifesting the properties for CIE validity.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:oropre:v:40:y:1992:i:5:p:898-913
    DOI: 10.1287/opre.40.5.898
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    Citations

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    Cited by:

    1. 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.
    2. Nilay Tanık Argon & Sigrún Andradóttir, 2006. "Replicated batch means for steady‐state simulations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(6), pages 508-524, September.
    3. 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.
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Halkos, George & Kevork, Ilias, 2002. "Confidence intervals in stationary autocorrelated time series," MPRA Paper 31840, University Library of Munich, Germany.
    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. Halkos, George & Kevork, Ilias, 2006. "Estimating population means in covariance stationary process," MPRA Paper 31843, University Library of Munich, Germany.
    13. Richard E. Nance & Robert G. Sargent, 2002. "Perspectives on the Evolution of Simulation," Operations Research, INFORMS, vol. 50(1), pages 161-172, February.

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