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Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling

Author

Listed:
  • Yijie Peng

    (Department of Management Science and Information Systems, Guanghua School of Management, Peking University, 100871 Beijing, China)

  • Michael C. Fu

    (Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

  • Bernd Heidergott

    (Department of Econometrics and Operations Research, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands)

  • Henry Lam

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

We propose a gradient-based simulated maximum likelihood estimation to estimate unknown parameters in a stochastic model without assuming that the likelihood function of the observations is available in closed form. A key element is to develop Monte Carlo–based estimators for the density and its derivatives for the output process, using only knowledge about the dynamics of the model. We present the theory of these estimators and demonstrate how our approach can handle various types of model structures. We also support our findings and illustrate the merits of our approach with numerical results.

Suggested Citation

  • Yijie Peng & Michael C. Fu & Bernd Heidergott & Henry Lam, 2020. "Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling," Operations Research, INFORMS, vol. 68(6), pages 1896-1912, November.
    • Handle: RePEc:inm:oropre:v:68:y:2020:i:6:p:1896-1912
    DOI: 10.1287/opre.2019.1978
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    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Vishal Gupta & Ioannis Ch. Paschalidis, 2012. "Inverse Optimization: A New Perspective on the Black-Litterman Model," Operations Research, INFORMS, vol. 60(6), pages 1389-1403, December.
    2. Bernd Heidergott & Warren Volk-Makarewicz, 2016. "A Measure-Valued Differentiation Approach to Sensitivities of Quantiles," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 293-317, February.
    3. Tsung-Yin Wang & Jau-Chuan Ke & Kuo-Hsiung Wang & Siu-Chuen Ho, 2006. "Maximum Likelihood Estimates and Confidence Intervals of an M/M/R Queue with Heterogeneous Servers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 371-384, May.
    4. Guangwu Liu & Liu Jeff Hong, 2009. "Kernel estimation of quantile sensitivities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 511-525, September.
    5. Basawa, I.V. & Bhat, U.N. & Zhou, J., 2008. "Parameter estimation using partial information with applications to queueing and related models," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1375-1383, September.
    6. Michael C. Fu & L. Jeff Hong & Jian-Qiang Hu, 2009. "Conditional Monte Carlo Estimation of Quantile Sensitivities," Management Science, INFORMS, vol. 55(12), pages 2019-2027, December.
    7. Michael C. Fu, 2015. "Stochastic Gradient Estimation," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 105-147, Springer.
    8. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    9. L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.
    10. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    11. Guangxin Jiang & Michael C. Fu, 2015. "Technical Note—On Estimating Quantile Sensitivities via Infinitesimal Perturbation Analysis," Operations Research, INFORMS, vol. 63(2), pages 435-441, April.
    12. L. Jeff Hong & Guangwu Liu, 2009. "Simulating Sensitivities of Conditional Value at Risk," Management Science, INFORMS, vol. 55(2), pages 281-293, February.
    13. Richard C. Larson, 1990. "The Queue Inference Engine: Deducing Queue Statistics from Transactional Data," Management Science, INFORMS, vol. 36(5), pages 586-601, May.
    14. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    15. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
    16. L. Jeff Hong & Guangwu Liu, 2010. "Pathwise Estimation of Probability Sensitivities Through Terminating or Steady-State Simulations," Operations Research, INFORMS, vol. 58(2), pages 357-370, April.
    17. Rajan Suri & Michael A. Zazanis, 1988. "Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue," Management Science, INFORMS, vol. 34(1), pages 39-64, January.
    18. John R. Birge & Ali Hortaçsu & J. Michael Pavlin, 2017. "Inverse Optimization for the Recovery of Market Structure from Market Outcomes: An Application to the MISO Electricity Market," Operations Research, INFORMS, vol. 65(4), pages 837-855, August.
    19. Yijie Peng & Michael C. Fu & Jian-Qiang Hu, 2016. "Gradient-based simulated maximum likelihood estimation for stochastic volatility models using characteristic functions," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1393-1411, September.
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    Cited by:

    1. Jiaqiao Hu & Yijie Peng & Gongbo Zhang & Qi Zhang, 2022. "A Stochastic Approximation Method for Simulation-Based Quantile Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 2889-2907, November.
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    4. Harsha Honnappa, 2022. "Calibrating nonstationary queueing network models," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 525-527, April.

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