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Measuring and testing dependence by correlation of distances. (English) Zbl 1129.62059
Summary: Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are discussed. Implementation of the test and Monte Carlo results are also presented.

62H20 Measures of association (correlation, canonical correlation, etc.)
62G10 Nonparametric hypothesis testing
65C05 Monte Carlo methods
62G20 Asymptotic properties of nonparametric inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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