Journal
ANNALS OF STATISTICS
Volume 35, Issue 6, Pages 2769-2794Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/009053607000000505
Keywords
distance correlation; distance covariance; multivariate independence
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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.
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