IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v36y1989i5p683-692.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198910)36:53.0.CO;2-L
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198910)36:53.0.CO;2-L?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. 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.
    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. 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.

    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. Kenneth W. Bauer & James R. Wilson, 1992. "Control‐variate selection criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 307-321, April.
    2. Wu, Junqi & Niu, Zhibin & Li, Xiang & Huang, Lizhen & Nielsen, Per Sieverts & Liu, Xiufeng, 2023. "Understanding multi-scale spatiotemporal energy consumption data: A visual analysis approach," Energy, Elsevier, vol. 263(PD).
    3. Lee, Jinkyu & Bae, Sanghyeon & Kim, Woo Chang & Lee, Yongjae, 2023. "Value function gradient learning for large-scale multistage stochastic programming problems," European Journal of Operational Research, Elsevier, vol. 308(1), pages 321-335.
    4. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen & Erik Schlögl, 2009. "Alternative Defaultable Term Structure Models," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(1), pages 1-31, March.
    5. Rayadurgam Srikant & Ward Whitt, 1999. "Variance Reduction in Simulations of Loss Models," Operations Research, INFORMS, vol. 47(4), pages 509-523, August.
    6. Rubinstein, Reuven Y., 1986. "The score function approach for sensitivity analysis of computer simulation models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 28(5), pages 351-379.
    7. Athanassios N. Avramidis & Kenneth W. Bauer & James R. Wilson, 1991. "Simulation of stochastic activity networks using path control variates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 183-201, April.
    8. Bo Hu & Matthias Dehmer & Frank Emmert-Streib & Bo Zhang, 2021. "Analysis of the real number of infected people by COVID-19: A system dynamics approach," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-9, March.
    9. Kevin S. Zhang & Traian A. Pirvu, 2020. "Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model," Papers 2006.07771, arXiv.org.
    10. Barry L. Nelson, 2004. "50th Anniversary Article: Stochastic Simulation Research in Management Science," Management Science, INFORMS, vol. 50(7), pages 855-868, July.
    11. Amano, Tomoyuki & Taniguchi, Masanobu, 2011. "Control variate method for stationary processes," Journal of Econometrics, Elsevier, vol. 165(1), pages 20-29.
    12. Chris J. Oates & Mark Girolami & Nicolas Chopin, 2017. "Control functionals for Monte Carlo integration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 695-718, June.
    13. Wilson, James R., 1983. "Variance reduction: The current state," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(1), pages 55-59.
    14. Schweinberger, Michael & Snijders, Tom A.B., 2007. "Markov models for digraph panel data: Monte Carlo-based derivative estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4465-4483, May.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:36:y:1989:i:5:p:683-692. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.