Contents
Which is the best definition of distance correlation?
Distance correlation. In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension.
When is the population distance correlation coefficient zero?
The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson’s correlation, which can only detect linear association between two random variables.
When did Gabor Szekely invent distance correlation?
Distance correlation was introduced in 2005 by Gábor J. Székely in several lectures to address this deficiency of Pearson’s correlation, namely that it can easily be zero for dependent variables. Correlation = 0 (uncorrelatedness) does not imply independence while distance correlation = 0 does imply independence.
How to find the correlation between X and Y?
The value ρXY is also called the correlation coefficient. Theorem 4.5.3 For any random variables X and Y, Cov(X,Y) = EXY −µXµY . ρXY = 0. Theorem 4.5.6 If X and Y are any two random variables and a and b are any two constants, then Var(aX +bY) = a 2VarX +b VarY +2abCov(X,Y).
How is distance correlation used in a permutation test?
Distance correlation can be used to perform a 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.
How is distance covariance and Pearson correlation obtained?
Distance correlation is obtained from the three numbers analogously how Pearson correlation is obtained from usual covariance and the pair of variances: divide the covariance by the sq. root of the product of two variances. Distance covariance (and correlation) is not the covariance (or correlation) between the distances themselves.