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Volume 4/Number 2, Summer 2010 Research Papers Area under the curve maximization method in credit scoring Kakeru Miura
The Graduate University for Advanced Studies, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan; email: kmiura@ism.ac.jp Satoshi Yamashita
The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan; email: yamasita@ism.ac.jp Shinto Eguchi
The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan; email: eguchi@ism.ac.jp The receiver operator characteristic curve and area under the curve (AUC) are widely used in credit risk scoring. In this field, it is common to employ the logit model with maximum likelihood estimators. The accuracy of the model is measured by AUC, but it turns out that the logit model with maximum likelihood (ML) estimators (which we refer to as the logit ML model) generally does not achieve optimality with respect to AUC. We propose a new method that uses AUC in a different manner. Our purpose is to estimate parameters and obtain a model for which AUC is maximized; we do this by using an approximated AUC as the objective function. We find that the model thus obtained is not only optimal with respect to AUC but also more robust than the original logit ML model when applied to data sets that include an outlier. Outliers are often present in financial indicator data, so our new method is very effective in terms of robustness.
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