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December 2014 Partial distance correlation with methods for dissimilarities
Gábor J. Székely, Maria L. Rizzo
Ann. Statist. 42(6): 2382-2412 (December 2014). DOI: 10.1214/14-AOS1255


Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions and applications of distance correlation have been discussed in the recent literature, but the problem of defining the partial distance correlation has remained an open question of considerable interest. The problem of partial distance correlation is more complex than partial correlation partly because the squared distance covariance is not an inner product in the usual linear space. For the definition of partial distance correlation, we introduce a new Hilbert space where the squared distance covariance is the inner product. We define the partial distance correlation statistics with the help of this Hilbert space, and develop and implement a test for zero partial distance correlation. Our intermediate results provide an unbiased estimator of squared distance covariance, and a neat solution to the problem of distance correlation for dissimilarities rather than distances.


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Gábor J. Székely. Maria L. Rizzo. "Partial distance correlation with methods for dissimilarities." Ann. Statist. 42 (6) 2382 - 2412, December 2014.


Published: December 2014
First available in Project Euclid: 20 October 2014

zbMATH: 1309.62105
MathSciNet: MR3269983
Digital Object Identifier: 10.1214/14-AOS1255

Primary: 62H15 , 62H20 , 62Hxx
Secondary: 62Gxx

Keywords: dissimilarity , energy statistics , independence , multivariate , partial distance correlation

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 6 • December 2014
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