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Consistency of the estimator of binary response models based on AUC maximization


  • Igor Fedotenkov



This paper examines the asymptotic properties of a binary response model estimator based on maximization of the Area Under receiver operating characteristic Curve (AUC). Given certain assumptions, AUC maximization is a consistent method of binary response model estimation up to normalizations. As AUC is equivalent to Mann-Whitney U statistics and Wilcoxon test of ranks, maximization of area under ROC curve is equivalent to the maximization of corresponding statistics. Compared to parametric methods, such as logit and probit, AUC maximization relaxes assumptions about error distribution, but imposes some restrictions on the distribution of explanatory variables, which can be easily checked, since this information is observable. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Igor Fedotenkov, 2013. "Consistency of the estimator of binary response models based on AUC maximization," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 381-390, August.
  • Handle: RePEc:spr:stmapp:v:22:y:2013:i:3:p:381-390
    DOI: 10.1007/s10260-013-0229-4

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    References listed on IDEAS

    1. Manski, Charles F, 1983. "Closest Empirical Distribution Estimation," Econometrica, Econometric Society, vol. 51(2), pages 305-319, March.
    2. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    3. Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
    4. Wenxia Ge & G. Whitmore, 2010. "Binary response and logistic regression in recent accounting research publications: a methodological note," Review of Quantitative Finance and Accounting, Springer, vol. 34(1), pages 81-93, January.
    5. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    6. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    7. Manski, Charles F., 1986. "Semiparametric analysis of binary response from response-based samples," Journal of Econometrics, Elsevier, vol. 31(1), pages 31-40, February.
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    More about this item


    ROC; AUC maximization; Consistency; Binary response model; 62G05; 62G20; 62J15;

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