Consistency of AUC Maximization as an Estimator of Binary Choice Models

This paper studies the asymptotic properties of the binary choice model estimator, based on the maximization of the Area Under receiver operating characteristic Curve (AUC). It is shown that under certain assumptions AUC maximization is a consistent method of binary choice models 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. Comparing with the parametric methods, such as logit and probit, AUC maximization relaxes assumptions about the distribution of errors, but imposes some restrictions on the distribution of regressors, which can be easily checked, since this information is observed