Two‐sample test based on classification probability

Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two‐sample test problem in the framework of classification. Based on the estimates of classification probabilities from a classifier trained from the samples, a test statistic is proposed. We explain why such a test can be a powerful test and compare its performance in terms of the power and efficiency with those of some other recently proposed tests with simulation and real‐life data. The test proposed is nonparametric and can be applied to complex and high‐dimensional data wherever there is a classifier that provides consistent estimate of the classification probability for such data.