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In this paper we deal with the problem of testing for the quality of $k$probability distributions. We introduce a generalization of the maximum meandiscrepancy that permits to characterize the null hypothesis. Then, anestimator of it is proposed as test statistic, and its asymptotic distributionunder the null hypothesis is derived. Simulations show that the introducedprocedure outperforms classical ones.

$k$-Sample problem based on generalized maximum mean discrepancy