IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v31y2019i3p445-458.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2018.0834
    Download Restriction: no

    File URL: https://libkey.io/10.1287/ijoc.2018.0834?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. 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.
    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. Wang, Xin & Kuo, Yong-Hong & Shen, Houcai & Zhang, Lianmin, 2021. "Target-oriented robust location–transportation problem with service-level measure," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 1-20.

    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. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    2. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    3. Jun-ya Gotoh & Michael Jong Kim & Andrew E. B. Lim, 2020. "Worst-case sensitivity," Papers 2010.10794, arXiv.org.
    4. Zhang, Hanxiao & Li, Yan-Fu, 2022. "Robust optimization on redundancy allocation problems in multi-state and continuous-state series–parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    5. Soonhui Lee & Tito Homem-de-Mello & Anton Kleywegt, 2012. "Newsvendor-type models with decision-dependent uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 189-221, October.
    6. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    7. Ruiwei Jiang & Siqian Shen & Yiling Zhang, 2017. "Integer Programming Approaches for Appointment Scheduling with Random No-Shows and Service Durations," Operations Research, INFORMS, vol. 65(6), pages 1638-1656, December.
    8. Gong, Hailei & Zhang, Zhi-Hai, 2022. "Benders decomposition for the distributionally robust optimization of pricing and reverse logistics network design in remanufacturing systems," European Journal of Operational Research, Elsevier, vol. 297(2), pages 496-510.
    9. Viet Anh Nguyen & Fan Zhang & Shanshan Wang & Jose Blanchet & Erick Delage & Yinyu Ye, 2021. "Robustifying Conditional Portfolio Decisions via Optimal Transport," Papers 2103.16451, arXiv.org, revised Apr 2024.
    10. Viet Anh Nguyen & Daniel Kuhn & Peyman Mohajerin Esfahani, 2018. "Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator," Papers 1805.07194, arXiv.org.
    11. Jiang, Sheng-Long & Wang, Meihong & Bogle, I. David L., 2023. "Plant-wide byproduct gas distribution under uncertainty in iron and steel industry via quantile forecasting and robust optimization," Applied Energy, Elsevier, vol. 350(C).
    12. Taozeng Zhu & Jingui Xie & Melvyn Sim, 2022. "Joint Estimation and Robustness Optimization," Management Science, INFORMS, vol. 68(3), pages 1659-1677, March.
    13. Shunichi Ohmori, 2021. "A Predictive Prescription Using Minimum Volume k -Nearest Neighbor Enclosing Ellipsoid and Robust Optimization," Mathematics, MDPI, vol. 9(2), pages 1-16, January.
    14. Manish Bansal & Yingqiu Zhang, 2021. "Scenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programs," Journal of Global Optimization, Springer, vol. 81(2), pages 391-433, October.
    15. Ken Kobayashi & Yuichi Takano & Kazuhide Nakata, 2021. "Bilevel cutting-plane algorithm for cardinality-constrained mean-CVaR portfolio optimization," Journal of Global Optimization, Springer, vol. 81(2), pages 493-528, October.
    16. Marcel-Ioan Boloș & Ioana-Alexandra Bradea & Camelia Delcea, 2021. "Optimization of Financial Asset Neutrosophic Portfolios," Mathematics, MDPI, vol. 9(11), pages 1-36, May.
    17. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    18. Xuan Wang & Jiawei Zhang, 2015. "Process Flexibility: A Distribution-Free Bound on the Performance of k -Chain," Operations Research, INFORMS, vol. 63(3), pages 555-571, June.
    19. Ben-Tal, A. & den Hertog, D. & De Waegenaere, A.M.B. & Melenberg, B. & Rennen, G., 2011. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Other publications TiSEM 4d43dc51-86d9-4804-8563-9, Tilburg University, School of Economics and Management.
    20. Pengyu Qian & Zizhuo Wang & Zaiwen Wen, 2015. "A Composite Risk Measure Framework for Decision Making under Uncertainty," Papers 1501.01126, arXiv.org.

    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:inm:orijoc:v:31:y:2019:i:3:p:445-458. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.