IDEAS home Printed from https://ideas.repec.org/p/azt/cemmap/16-25.html
   My bibliography  Save this paper

Binary classification with the maximum score model and linear programming

Author

Listed:
  • Joel L. Horowitz
  • Sokbae Lee

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.

Suggested Citation

  • Joel L. Horowitz & Sokbae Lee, 2025. "Binary classification with the maximum score model and linear programming," CeMMAP working papers 16/25, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:16/25
    DOI: 10.47004/wp.cem.2025.1625
    as

    Download full text from publisher

    File URL: https://cemmap.ac.uk/wp-content/uploads/2025/08/CWP1625-Binary-classification-with-the-maximum-score-model-and-linear-programming.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.47004/wp.cem.2025.1625?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
    ---><---

    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. 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.
    3. 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.
    4. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    5. 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.
    6. 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.
    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. Chen, Songnian & Zhang, Hanghui, 2015. "Binary quantile regression with local polynomial smoothing," Journal of Econometrics, Elsevier, vol. 189(1), pages 24-40.
    3. Gyungbae Park, 2024. "Debiased Machine Learning when Nuisance Parameters Appear in Indicator Functions," Papers 2403.15934, arXiv.org, revised Mar 2025.
    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. Toru Kitagawa & Shosei Sakaguchi & Aleksey Tetenov, 2021. "Constrained Classification and Policy Learning," Papers 2106.12886, arXiv.org, revised Jul 2023.
    6. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    7. repec:cep:stiecm:em/2012/559 is not listed on IDEAS
    8. 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.
    9. Mariagiovanna Baccara & Ayse Imrohoroglu & Alistair J. Wilson & Leeat Yariv, 2012. "A Field Study on Matching with Network Externalities," American Economic Review, American Economic Association, vol. 102(5), pages 1773-1804, August.
    10. Matias D. Cattaneo & Michael Jansson & Kenichi Nagasawa, 2020. "Bootstrap‐Based Inference for Cube Root Asymptotics," Econometrica, Econometric Society, vol. 88(5), pages 2203-2219, September.
    11. 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.
    12. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    13. Madden, Gary & Mayer, Walter & Wu, Chen & Tran, Thien, 2015. "The forecasting accuracy of models of post-award network deployment: An application of maximum score tests," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1153-1158.
    14. 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.
    15. Horowitz, Joel L., 2004. "Semiparametric models," Papers 2004,17, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    16. Le‐Yu Chen & Sokbae Lee & Myung Jae Sung, 2014. "Maximum score estimation with nonparametrically generated regressors," Econometrics Journal, Royal Economic Society, vol. 17(3), pages 271-300, October.
    17. 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.
    18. 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.
    19. 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.
    20. Mayer Walter J. & Wu Chen, 2013. "A maximum score test for binary response models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(5), pages 619-639, December.
    21. Jeremy T. Fox, 2007. "Semiparametric estimation of multinomial discrete-choice models using a subset of choices," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1002-1019, December.

    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:azt:cemmap:16/25. 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: Dermot Watson (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.