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Robust Maximum Likelihood Estimation

Author

Listed:
  • Dimitris Bertsimas

    (Operations Research Center and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139;)

  • Omid Nohadani

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

In many applications, statistical estimators serve to derive conclusions from data, for example, in finance, medical decision making, and clinical trials. However, the conclusions are typically dependent on uncertainties in the data. We use robust optimization principles to provide robust maximum likelihood estimators that are protected against data errors. Both types of input data errors are considered: (a) the adversarial type, modeled using the notion of uncertainty sets, and (b) the probabilistic type, modeled by distributions. We provide efficient local and global search algorithms to compute the robust estimators and discuss them in detail for the case of multivariate normally distributed data. The estimator performance is demonstrated on two applications. First, using computer simulations, we demonstrate that the proposed estimators are robust against both types of data uncertainty and provide more accurate estimates compared with classical estimators, which degrade significantly, when errors are encountered. We establish a range of uncertainty sizes for which robust estimators are superior. Second, we analyze deviations in cancer radiation therapy planning. Uncertainties among plans are caused by patients’ individual anatomies and the trial-and-error nature of the process. When analyzing a large set of past clinical treatment data, robust estimators lead to more reliable decisions when applied to a large set of past treatment plans.

Suggested Citation

  • Dimitris Bertsimas & Omid Nohadani, 2019. "Robust Maximum Likelihood Estimation," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 445-458, July.
  • Handle: RePEc:inm:orijoc:v:31:y:2019:i:3:p:445-458
    DOI: 10.1287/ijoc.2018.0834
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    References listed on IDEAS

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    1. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    2. Dimitris Bertsimas & Omid Nohadani, 2010. "Robust optimization with simulated annealing," Journal of Global Optimization, Springer, vol. 48(2), pages 323-334, October.
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    Cited by:

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