On the optimal binary classifier with an application

The alternative accumulated improvement curve stochastic order is a criterion for the comparison of the performance of classifiers that predict binary responses. An explicit optimal classifier for this criterion is obtained. That optimal classifier has the largest ROC and CAP curves and indexes, that is, it is also optimal for the criteria based on the comparison of such curves and indexes. An application of the results to the search of the best classifier to predict clients of a bank which will make a transaction in the future is developed.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).