Open Access
December 2007 Measuring and testing dependence by correlation of distances
Gábor J. Székely, Maria L. Rizzo, Nail K. Bakirov
Ann. Statist. 35(6): 2769-2794 (December 2007). DOI: 10.1214/009053607000000505


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.


Download Citation

Gábor J. Székely. Maria L. Rizzo. Nail K. Bakirov. "Measuring and testing dependence by correlation of distances." Ann. Statist. 35 (6) 2769 - 2794, December 2007.


Published: December 2007
First available in Project Euclid: 22 January 2008

zbMATH: 1129.62059
MathSciNet: MR2382665
Digital Object Identifier: 10.1214/009053607000000505

Primary: 62G10
Secondary: 62H20

Keywords: Distance correlation , distance covariance , multivariate independence

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • December 2007
Back to Top