### Measuring and testing dependence by correlation of distances

Gábor J. Székely, Maria L. Rizzo, and Nail K. Bakirov
Source: Ann. Statist. Volume 35, Number 6 (2007), 2769-2794.

#### Abstract

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are discussed. Implementation of the test and Monte Carlo results are also presented.

First Page:
Primary Subjects: 62G10
Secondary Subjects: 62H20
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.aos/1201012979
Digital Object Identifier: doi:10.1214/009053607000000505
Mathematical Reviews number (MathSciNet): MR2382665
Zentralblatt MATH identifier: 1129.62059

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