Revision as of 22:01, 10 November 2017 edit Drbabinski (talk \| contribs) 5 edits - updated intro to be more approachable for non-experts. larger focus on the ability to detect linear + nonlinear interactions, how dcorr can be used as a statistical test, and more scope for dcorr (i.e., kernel based methods, and its use in CCA and ICA) ← Previous edit		Revision as of 14:37, 16 November 2017 edit undo Mathstat (talk \| contribs) Extended confirmed users 959 edits Revise lede to be more understandable to non-experts. Next edit →
Line 1: In [[statistics]] and in [[probability theory]], '''distance correlation''' or '''distance covariance''' is a measure of [[~~statistical~~ dependence]] between two paired [[random vector]]s of arbitrary, not necessarily equal, [[Euclidean vector\|dimension]]. InThe ~~the limit of an infinite number of samples, the~~population distance correlation coefficient is zero if and only if the random vectors are [[~~statistically~~ independent]]. Thus, distance correlation ~~can detect~~measures both linear and nonlinear ~~interactions~~association between two random variables or random vectors. This is in contrast to [[Pearson's correlation]], which can only detect linear ~~interactions~~association between two [[random variable]]s. Distance correlation can be used to perform a [[Statistical hypothesis testing\|statistical test]] of dependence with a [[permutation test]]. One first computes the distance correlation (involving the re-centering of Euclidean distance matrices) between two random vectors, and then compares this value to the distance correlations of many shuffles of the data.

Distance correlation: Difference between revisions