Distance correlation

<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a> and in <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, distance correlation or distance covariance is a measure of <a href="/facts/Independence_(probability_theory)/NUzQtnUL">dependence</a> between two paired <a href="/facts/Random_vector/qMfooyVf">random vectors</a> of arbitrary, not necessarily equal, <a href="/facts/Euclidean_vector/bCLrdksy">dimension</a>. The population distance correlation coefficient is zero if and only if the random vectors are <a href="/facts/Independence_(probability_theory)/NUzQtnUL">independent</a>.  Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors.  This is in contrast to <a href="/facts/Pearson%2527s_correlation/Igf0xDPc">Pearson's correlation</a>, which can only detect linear association between two <a href="/facts/Random_variable/TwTBXnLT">random variables</a>.
</p><p>Distance correlation can be used to perform a <a href="/facts/Statistical_hypothesis_testing/yv9RPF6U">statistical test</a> of dependence with a <a href="/facts/Permutation_test/yq6LXqnX">permutation test</a>.  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.  
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Distance correlation open-in-new

Distance correlation