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Multivariate Hoeffding's Phi-Squared

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Nonparametric measure of multivariate association.

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Nonparametric measure of multivariate dependence between several random variables proposed in Gaißer, Ruppert & Schmid (2010). Unlike Pearson's or rank correlation (Kendall's tau, Spearman's rho), it picks up dependence of any form.

> multphi2(data)


data - n x d matrix containing n realizations of d random variables, association between which is to be measures.

Output: phi - 1x1 measure of association (phi = 0 corresponds to mutual independence of variables in columns of data, phi = 1 - increasing deterministic (not necessarily linear) relationship.


Gaißer, S., Ruppert, M., & Schmid, F. (2010). A multivariate version of Hoeffding’s Phi-Square. Journal of Multivariate Analysis, 101(10), 2571-2586.

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