A Class of Probability Metrics and its Statistical Applications

By L. Klebanov. 2002

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Prototypal Analysis and Prototypal Regression (2017, background): “e energy distance DED (Sz´ekely and Rizzo, 2013; Rizzo and Sz´ekely, 2016): D2 ED(µ 1(·),µ 2(·)) =2 Z X×X kx −x kdµ (x )dµ (x )− Z X×X kx −x kdµ (x )dµ (x ) − Z X×X kx1−x2kdµ2(x1)dµ2(x2) is proved in Klebanov (2002) to yield a metric, implying that the energy distance kernel induces an injective emb”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, background): “, in robust statistics [83], microarray data analysis [155], material structure analysis [9], etc.”