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The affinely invariant distance correlation

Székely, Rizzo and Bakirov (Ann. Statist. 35 (2007) 2769-2794) and Székely and Rizzo (Ann. Appl. Statist. 3 (2009) 1236-1265), in two seminal papers, introduced the powerful concept of distance correlation as a measure of dependence between sets of random variables. We study in this paper an affin...

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Bibliographic Details
Main Authors: Dueck, Johannes (Author) , Edelmann, Dominic (Author) , Gneiting, Tilmann (Author)
Format: Article (Journal)
Language:English
Published: 19 September 2014
In: Bernoulli
Year: 2014, Volume: 20, Issue: 4, Pages: 2305-2330
ISSN:1573-9759
DOI:10.3150/13-BEJ558
Online Access:Verlag, Volltext: http://dx.doi.org/10.3150/13-BEJ558
Verlag, Volltext: http://projecteuclid.org/euclid.bj/1411134461
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Author Notes:Johannes Dueck, Dominic Edelmann, Tilmann Gneiting and Donald Richards
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Summary:Székely, Rizzo and Bakirov (Ann. Statist. 35 (2007) 2769-2794) and Székely and Rizzo (Ann. Appl. Statist. 3 (2009) 1236-1265), in two seminal papers, introduced the powerful concept of distance correlation as a measure of dependence between sets of random variables. We study in this paper an affinely invariant version of the distance correlation and an empirical version of that distance correlation, and we establish the consistency of the empirical quantity. In the case of subvectors of a multivariate normally distributed random vector, we provide exact expressions for the affinely invariant distance correlation in both finite-dimensional and asymptotic settings, and in the finite-dimensional case we find that the affinely invariant distance correlation is a function of the canonical correlation coefficients. To illustrate our results, we consider time series of wind vectors at the Stateline wind energy center in Oregon and Washington, and we derive the empirical auto and cross distance correlation functions between wind vectors at distinct meteorological stations.
Item Description:Gesehen am 24.05.2018
Physical Description:Online Resource
ISSN:1573-9759
DOI:10.3150/13-BEJ558

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