Measuring and testing dependence by correlation of distances

Understand

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.