Making classifier performance comparisons when ROC curves intersect

The ROC curve is one of the most common statistical tools useful to assess classifier performance. The selection of the best classifier when ROC curves intersect is quite challenging. A novel approach for model comparisons when ROC curves show intersections is proposed. In particular, the relationship between ROC orderings and stochastic dominance is investigated in a theoretical framework and a general class of indicators is proposed which is coherent with dominance criteria also when ROC curves cross. Furthermore, a simulation study and a real application to credit risk data are proposed to illustrate the use of the new methodological approach.