BALL DIVERGENCE: NONPARAMETRIC TWO SAMPLE TEST.

ABSTRACT: In this paper, we first introduce Ball Divergence, a novel measure of the difference between two probability measures in separable Banach spaces, and show that the Ball Divergence of two probability measures is zero if and only if these two probability measures are identical without any moment assumption. Using Ball Divergence, we present a metric rank test procedure to detect the equality of distribution measures underlying independent samples. It is therefore robust to outliers or heavy-tail data. We show that this multivariate two sample test statistic is consistent with the Ball Divergence, and it converges to a mixture of χ² distributions under the null hypothesis and a normal distribution under the alternative hypothesis. Importantly, we prove its consistency against a gen

SUBMITTER: Pan W 

PROVIDER: S-EPMC6192286 | biostudies-literature | 2018 Jun

REPOSITORIES: biostudies-literature