The affinely invariant distance correlation
The affinely invariant distance correlation
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DOI：
10.3150/13-bej558
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发表时间：
2014-11-01
期刊：
影响因子：
1.5
通讯作者：
Richards, Donald
中科院分区：
文献类型：
--
作者：
Dueck, Johannes;Edelmann, Dominic;Richards, Donald
Szekely，Rizzo and Bakirov（Ann. Statist. 35（2007）2769-2794）和Szekely和Rizzo（Ann. Appl. Statist. 3（2009）1236-1265）在两篇开创性论文中介绍了作为随机变量集合之间的依赖性的度量的距离相关性的强大概念。本文研究了距离相关性的仿射不变版本和距离相关性的经验版本，并建立了经验量的一致性。在一个多元正态分布的随机向量的子向量的情况下，我们提供了精确的表达式的affiliate不变的距离相关在有限维和渐近设置，并在有限维的情况下，我们发现affiliate不变的距离相关是一个函数的典型相关系数。为了说明我们的研究结果，我们考虑在俄勒冈州和华盛顿的斯塔特林风能中心的风矢量的时间序列，我们推导出经验的自动和交叉距离相关函数风矢量在不同的气象站。
Szekely, Rizzo and Bakirov (Ann. Statist. 35 (2007) 2769-2794) and Szekely 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.