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A Basic Treatment of the Distance Covariance

Dominic Edelmann (), Tobias Terzer () and Donald Richards ()
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Dominic Edelmann: German Cancer Research Center
Tobias Terzer: German Cancer Research Center
Donald Richards: Pennsylvania State University

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 2, 12-25

Abstract: Abstract The distance covariance of Székely et al. (Ann. Statist., 35, 2769–2794 2007, 2009), a powerful measure of dependence between sets of multivariate random variables, has the crucial feature that it equals zero if and only if the sets are mutually independent. Hence the distance covariance can be applied to multivariate data to detect arbitrary types of non-linear associations between sets of variables. We provide in this article a basic, albeit rigorous, introductory treatment of the distance covariance. Our investigations yield an approach that can be used as the foundation for presentation of this important and timely topic even in advanced undergraduate- or junior graduate-level courses on mathematical statistics.

Keywords: Asymptotic distribution; Distance correlation; Multivariate tests of independence; Orthogonal transformations; U-statistics; Primary 62G10, 62H20; Secondary 60E10, 62G20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13571-021-00248-z

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