Asymptotic normality of a generalized maximum mean discrepancy estimator

Abstract

In this paper, we propose an estimator of the generalized maximum mean discrepancy between several probability distributions, constructed by modifying a naive estimator. Asymptotic normality is obtained for this estimator both under equality of these distributions and under the alternative hypothesis, so allowing to achieve a k-sample test for equality of distributions. A simulation study that allows to compare the proposed test to existing ones is provided.