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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

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    Cited by:

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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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