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Efficiency of Multivariate Control Variates in Monte Carlo Simulation

Author

Listed:
  • Reuven Y. Rubinstein

    (Technion, Istrael Institute of Technology, Haifa, Israel)

  • Ruth Marcus

    (Agricultural Research Organization, Beth-Dagan, Israel)

Abstract

This paper considers some statistical aspects of applying control variates to achieve variance reduction in the estimation of a vector of response variables in Monte Carlo simulation. It gives a result that quantifies the loss in variance reduction caused by the estimation of the optimal control matrix. For the one-dimensional case, we derive analytically the optimal size of the vector of control variates under specific assumptions on the covariance matrix. For the multidimensional case, our numerical results show that good variance reduction is achieved when the number of control variates is relatively small (approximately of the same order as the number of unknown parameters). Finally, we give some recommendations for future research.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:3:p:661-677
    DOI: 10.1287/opre.33.3.661
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    Citations

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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. Amano, Tomoyuki & Taniguchi, Masanobu, 2011. "Control variate method for stationary processes," Journal of Econometrics, Elsevier, vol. 165(1), pages 20-29.
    6. 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.
    7. Kevin S. Zhang & Traian A. Pirvu, 2020. "Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model," Papers 2006.07771, arXiv.org.
    8. 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.
    9. 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.
    10. 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.

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