Annals of Statistics

Measuring and testing dependence by correlation of distances

Gábor J. Székely, Maria L. Rizzo, and Nail K. Bakirov

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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.

Article information

Ann. Statist., Volume 35, Number 6 (2007), 2769-2794.

First available in Project Euclid: 22 January 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)

Distance correlation distance covariance multivariate independence


Székely, Gábor J.; Rizzo, Maria L.; Bakirov, Nail K. Measuring and testing dependence by correlation of distances. Ann. Statist. 35 (2007), no. 6, 2769--2794. doi:10.1214/009053607000000505.

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