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A criterion for the comparison of binary classifiers based on a stochastic dominance with an application to the sale of home insurances. (English) Zbl 1422.91362

Summary: Binary classification is an essential matter in multiple real-life problems, and so, the comparison of the performance of classifiers is a key issue. A criterion for that purpose is introduced in this manuscript. That criterion is based on a stochastic dominance, and permits to compare classifiers in subgroups of the population with the same size. By means of the new criterion, the alteration of the size of the subgroups where classifiers are compared, does not entail the modification of the suitable classifier. Characterization results of the criterion are proved. For that purpose, connections of the criterion with the theory of copulas, and with a tool introduced in the manuscript, the so-called continuity modelling vector, are essential. An application to the comparison of some classifiers for the detection of purchasers of home insurances is developed.

MSC:

91B30 Risk theory, insurance (MSC2010)
60E15 Inequalities; stochastic orderings
62P05 Applications of statistics to actuarial sciences and financial mathematics
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