IDEAS home Printed from https://ideas.repec.org/p/ifs/ifsewp/cwp16-24.html
   My bibliography  Save this paper

Binary classification with the maximum score model and linear programming

Author

Listed:
  • Joel L. Horowitz

    (Institute for Fiscal Studies)

  • Sokbae Lee

    (Institute for Fiscal Studies)

Abstract

This paper presents a computationally efficient method for binary classification using Manski's (1975,1985) maximum score model when covariates are discretely distributed and parameters are partially but not point identified. We establish conditions under which it is minimax optimal to allow for either non-classification or random classification and derive finite-sample and asymptotic lower bounds on the probability of correct classification. We also describe an extension of our method to continuous covariates. Our approach avoids the computational difficulty of maximum score estimation by reformulating the problem as two linear programs. Compared to parametric and nonparametric methods, our method balances extrapolation ability with minimal distributional assumptions. Monte Carlo simulations and empirical applications demonstrate its effectiveness and practical relevance.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Joel L. Horowitz & Sokbae Lee, 2025. "Binary classification with the maximum score model and linear programming," IFS Working Papers WCWP16/24, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:ifsewp:cwp16/24
    as

    Download full text from publisher

    File URL: https://ifs.org.uk/sites/default/files/2025-08/CWP1625-Binary-classification-with-the-maximum-score-model-and-linear-programming.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Delgado, Miguel A. & Rodriguez-Poo, Juan M. & Wolf, Michael, 2001. "Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator," Economics Letters, Elsevier, vol. 73(2), pages 241-250, November.
    2. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    3. Emily Breza & Arun G. Chandrasekhar & Davide Viviano, 2025. "Generalizability with ignorance in mind: learning what we do (not) know for archetypes discovery," Papers 2501.13355, arXiv.org, revised Jul 2025.
    4. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    5. Dries F. Benoit & Dirk Van den Poel, 2012. "Binary quantile regression: a Bayesian approach based on the asymmetric Laplace distribution," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(7), pages 1174-1188, November.
    6. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    Full references (including those not matched with items on IDEAS)

    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. Chen, Le-Yu & Lee, Sokbae, 2018. "Best subset binary prediction," Journal of Econometrics, Elsevier, vol. 206(1), pages 39-56.
    2. Nan Liu & Yanbo Liu & Yuya Sasaki & Yuanyuan Wan, 2025. "Nonparametric Uniform Inference in Binary Classification and Policy Values," Papers 2511.14700, arXiv.org, revised Dec 2025.
    3. Chen, Songnian & Zhang, Hanghui, 2015. "Binary quantile regression with local polynomial smoothing," Journal of Econometrics, Elsevier, vol. 189(1), pages 24-40.
    4. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1025-1106, Elsevier.
    5. repec:cep:stiecm:em/2012/559 is not listed on IDEAS
    6. Chen, Le-Yu & Oparina, Ekaterina & Powdthavee, Nattavudh & Srisuma, Sorawoot, 2022. "Robust Ranking of Happiness Outcomes: A Median Regression Perspective," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 672-686.
    7. Aristotelis Epanomeritakis & Davide Viviano, 2025. "Learning What to Learn: Experimental Design when Combining Experimental with Observational Evidence," Papers 2510.23434, arXiv.org, revised Dec 2025.
    8. D. F. Benoit & D. Van Den Poel, 2010. "Binary quantile regression: A Bayesian approach based on the asymmetric Laplace density," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 10/662, Ghent University, Faculty of Economics and Business Administration.
    9. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    10. Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2016. "Informational content of special regressors in heteroskedastic binary response models," Journal of Econometrics, Elsevier, vol. 193(1), pages 162-182.
    11. Jason R. Blevins, 2013. "Non-Standard Rates of Convergence of Criterion-Function-Based Set Estimators," Working Papers 13-02, Ohio State University, Department of Economics.
    12. Alistair Wilson & Mariagiovanna Baccara & Ayse Imrohoroglu & Leeat Yariv, 2009. "A Field Study on Matching with Network Externalities," Working Paper 486, Department of Economics, University of Pittsburgh, revised Sep 2011.
    13. Tatiana Komarova, 2012. "Binary Choice Models with Discrete Regressors: Identification and Misspecification," STICERD - Econometrics Paper Series 559, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. Xun Tang, 2009. "Binary Regressions with Bounded Median Dependence," PIER Working Paper Archive 09-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    15. Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," ANU Working Papers in Economics and Econometrics 2020-671, Australian National University, College of Business and Economics, School of Economics.
    16. Wan, Yuanyuan & Xu, Haiqing, 2015. "Inference in semiparametric binary response models with interval data," Journal of Econometrics, Elsevier, vol. 184(2), pages 347-360.
    17. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    18. Kenta Takatsu & Arun Kumar Kuchibhotla, 2025. "Bridging Root-$n$ and Non-standard Asymptotics: Adaptive Inference in M-Estimation," Papers 2501.07772, arXiv.org, revised Apr 2025.
    19. Vira Semenova, 2023. "Debiased Machine Learning of Aggregated Intersection Bounds and Other Causal Parameters," Papers 2303.00982, arXiv.org, revised May 2025.
    20. repec:cep:stiecm:/2012/559 is not listed on IDEAS
    21. Lee, Sokbae & Seo, Myung Hwan, 2008. "Semiparametric estimation of a binary response model with a change-point due to a covariate threshold," Journal of Econometrics, Elsevier, vol. 144(2), pages 492-499, June.
    22. Le-Yu Chen & Sokbae (Simon) Lee & Myung Jae Sung, 2013. "Maximum score estimation of preference parameters for a binary choice model under uncertainty," CeMMAP working papers CWP14/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ifs:ifsewp:cwp16/24. 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: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/ifsssuk.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.