The affinely invariant distance correlation

Johannes Dueck, Dominic Edelmann, Tilmann Gneiting, Donald Richards

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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 finitedimensional 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.

Original languageEnglish (US)
Pages (from-to)2305-2330
Number of pages26
JournalBernoulli
Volume20
Issue number4
DOIs
StatePublished - Nov 1 2014

Fingerprint

Invariant
Measures of Dependence
Canonical Correlation
Wind Energy
Distance Function
Random Vector
Correlation coefficient
Correlation Function
Time series
Random variable
Distinct

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Dueck, J., Edelmann, D., Gneiting, T., & Richards, D. (2014). The affinely invariant distance correlation. Bernoulli, 20(4), 2305-2330. https://doi.org/10.3150/13-BEJ558
Dueck, Johannes ; Edelmann, Dominic ; Gneiting, Tilmann ; Richards, Donald. / The affinely invariant distance correlation. In: Bernoulli. 2014 ; Vol. 20, No. 4. pp. 2305-2330.
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Dueck, J, Edelmann, D, Gneiting, T & Richards, D 2014, 'The affinely invariant distance correlation', Bernoulli, vol. 20, no. 4, pp. 2305-2330. https://doi.org/10.3150/13-BEJ558

The affinely invariant distance correlation. / Dueck, Johannes; Edelmann, Dominic; Gneiting, Tilmann; Richards, Donald.

In: Bernoulli, Vol. 20, No. 4, 01.11.2014, p. 2305-2330.

Research output: Contribution to journalArticle

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Dueck J, Edelmann D, Gneiting T, Richards D. The affinely invariant distance correlation. Bernoulli. 2014 Nov 1;20(4):2305-2330. https://doi.org/10.3150/13-BEJ558