On the three-way equivalence of AUC in credit scoring with tied scores

ABSTRACT

In credit scoring, it is well known that AUC (the area under curve) can be calculated geometrically, by the probability of a correct ranking of a good and bad pair, and by the Wilcoxon Rank-Sum statistic. This three-way equivalence was first present by Hanley and McNeil in 1982 without considering tied scores and without giving analytical proofs. In this paper, we extend the three-way equivalence to the case with tied scores and provide analytic proofs for the three-way equivalence.

KEYWORDS:

• Concordant pair
• Discordant pair
• Receiver operating characteristic (ROC)
• Tied pair
• The area under curve (AUC)
• Wilcoxon rank-sum statistic.