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The optimal linear combination of control variates in the presence of asymptotically negligible bias

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  • Peter W. Glynn
  • Donald L. Iglehart

Abstract

The optimal linear combination of control variates is well known when the controls are assumed to be unbiased. We derive here the optimal linear combination of controls in the situation where asymptotically negligible bias is present. The small‐sample linear control which minimizes the mean square error (MSE) is derived. When the optimal asymptotic linear control is used rather than the optimal small‐sample control, the degradation in MSE is c/n3, where n is the sample size and c is a known constant. This analysis is particulary relevant to the small‐sample theory for control variates as applied to the steady‐state estimation problem. Results for the method of multiple estimates are also given.

Suggested Citation

  • Peter W. Glynn & Donald L. Iglehart, 1989. "The optimal linear combination of control variates in the presence of asymptotically negligible bias," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 683-692, October.
  • Handle: RePEc:wly:navres:v:36:y:1989:i:5:p:683-692
    DOI: 10.1002/1520-6750(198910)36:53.0.CO;2-L
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    References listed on IDEAS

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    1. Reuven Y. Rubinstein & Ruth Marcus, 1985. "Efficiency of Multivariate Control Variates in Monte Carlo Simulation," Operations Research, INFORMS, vol. 33(3), pages 661-677, June.
    2. Stephen S. Lavenberg & Thomas L. Moeller & Peter D. Welch, 1982. "Statistical Results on Control Variables with Application to Queueing Network Simulation," Operations Research, INFORMS, vol. 30(1), pages 182-202, February.
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    Cited by:

    1. Saralees Nadarajah & Samuel Kotz, 2007. "On the Linear Combination of Laplace and Logistic Random Variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(2), pages 185-194.

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