BROWNIAN DISTANCE COVARIANCE

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classica...

Full description

Saved in:
Bibliographic Details
Published in:The annals of applied statistics 2009-12, Vol.3 (4), p.1236-1265
Main Authors: Székely, Gábor J., Rizzo, Maria L.
Format: Article
Language:English
Subjects:
Brownian covariance
Brownian motion
Correlations
Covariance
dcor
Distance correlation
Distribution theory
Eigenfunctions
Exact sciences and technology
independence
Markov processes
Mathematical vectors
Mathematics
multivariate
Multivariate analysis
Probability and statistics
Probability theory and stochastic processes
Random variables
Sample size
Sciences and techniques of general use
Statistical theories
Statistics
Stochastic processes
Weighting functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero if and only if the random vectors are independent. The notion of covariance with respect to a stochastic process is introduced, and it is shown that population distance covariance coincides with the covariance with respect to Brownian motion; thus, both can be called Brownian distance covariance. In the bivariate case, Brownian covariance is the natural extension of product-moment covariance, as we obtain Pearson product-moment covariance by replacing the Brownian motion in the definition with identity. The corresponding statistic has an elegantly simple computing formula. Advantages of applying Brownian covariance and correlation vs the classical Pearson covariance and correlation are discussed and illustrated.
ISSN:1932-6157
1941-7330
DOI:10.1214/09-AOAS312