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
Citation
Wenliang Pan. Yuan Tian. Xueqin Wang. Heping Zhang. "Ball Divergence: Nonparametric two sample test." Ann. Statist. 46 (3) 1109 - 1137, June 2018. https://doi.org/10.1214/17-AOS1579
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