Distance correlation: Difference between revisions

Revision as of 05:57, 11 September 2017

Revision as of 13:55, 12 October 2017

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This identity shows that the distance covariance is not the same as the covariance of distances, {{nowrap|cov({{norm|''X'' − ''X' ''}}, {{norm|''Y'' − ''Y' '' }}}}). This can be zero even if ''X'' and ''Y'' are not independent.

Alternatively, the squared distance covariance can be defined as the weighted [[Norm (mathematics)#Euclidean_norm|''L''² norm]] of the distance between the joint [[Characteristic function (probability theory)|characteristic function]] of the random variables and the product of their marginal characteristic functions:<ref name=SR2009a>Székely & Rizzo (2009) Theorem 7, (3.7), p. 1249.</ref>

: <math>