The Annals of Statistics
- Ann. Statist.
- Volume 35, Number 6 (2007), 2769-2794.
Measuring and testing dependence by correlation of distances
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.
Ann. Statist., Volume 35, Number 6 (2007), 2769-2794.
First available in Project Euclid: 22 January 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G10: Hypothesis testing
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)
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. https://projecteuclid.org/euclid.aos/1201012979