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Derandomizing Variance Estimators

Author

Listed:
  • Shane G. Henderson

    (University of Auckland, Auckland, New Zealand)

  • Peter W. Glynn

    (Department of Engineering—Economic Systems and Operations Research, Stanford University, Stanford, California, 94305)

Abstract

One may consider a discrete-event simulation as a Markov chain evolving on a suitably rich state space. One way that regenerative cycles may be constructed for general state-space Markov chains is to generate auxiliary coin-flip random variables at each transition, with a regeneration occurring if the coin-flip results in a success. The regenerative cycles are therefore randomized with respect to the sequence of states visited by the Markov chain. The point estimator for a steady-state performance measure does not depend on the cycle structure of the chain, but the variance estimator (that defines the width of a confidence interval for the performance measure) does. This implies that the variance estimator is randomized with respect to the visited states. We show how to “derandomize” the variance estimator through the use of conditioning. A new variance estimator is obtained that is consistent and has lower variance than the standard estimator.

Suggested Citation

  • Shane G. Henderson & Peter W. Glynn, 1999. "Derandomizing Variance Estimators," Operations Research, INFORMS, vol. 47(6), pages 907-916, December.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:6:p:907-916
    DOI: 10.1287/opre.47.6.907
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    References listed on IDEAS

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    1. Peter W. Glynn & Donald L. Iglehart, 1993. "Notes: Conditions for the Applicability of the Regenerative Method," Management Science, INFORMS, vol. 39(9), pages 1108-1111, September.
    2. Ward Whitt, 1980. "Continuity of Generalized Semi-Markov Processes," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 494-501, November.
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