Measuring and testing dependence by correlation of distances

@article{Szekely2007MeasuringAT,
  title={Measuring and testing dependence by correlation of distances},
  author={G'abor J. Sz'ekely and Maria L. Rizzo and Nail K. Bakirov},
  journal={Annals of Statistics},
  year={2007},
  volume={35},
  pages={2769-2794}
}
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… 

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