Consistency of the estimator of binary response models based on AUC maximization
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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.
KeywordsROC AUC maximization Consistency Binary response model
Mathematics Subject Classification (2010)62G05 62G20 62J15
I would like to thank the participants at the 12th Symposium of Mathematics and its Applications (2009) in Timisoara. Furthermore, I wish to thank Alfredas Račkauskas, Dmitrij Celov and Irena Mikolajun for their useful comments and Steve Guttenberg for his help with the English language.
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