Distance correlation: Difference between revisions

Revision as of 19:09, 15 August 2014

Revision as of 13:56, 29 December 2014

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(ii) <math>\operatorname{dCor}(X,Y) = 0</math> if and only if <math>X</math> and <math>Y</math> are independent.

(iii) <math>\operatorname{dCor}_n(X,Y) = 1</math> implies that dimensions of the linear spacessubspaces spanned by <math>X</math> and <math>Y</math> samples respectively are almost surely equal and if we assume that these subspaces are equal, then in this subspace <math>Y = A + b\,\mathbf{C}X</math> for some vector <math>A</math>, scalar <math>b</math>, and [[orthonormal matrix]] <math>\mathbf{C}</math>.

===Distance covariance===