DISTANCE COVARIANCE IN METRIC SPACES
成果类型：
Article
署名作者：
Lyons, Russell
署名单位：
Indiana University System; Indiana University Bloomington
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/12-AOP803
发表日期：
2013
页码：
3284-3305
关键词：
摘要：
We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Szekely, Rizzo and Bakirov, to general metric spaces. We show that for testing independence, it is necessary and sufficient that the metric space be of strong negative type. In particular, we show that this holds for separable Hilbert spaces, which answers a question of Kosorok. Instead of the manipulations of Fourier transforms used in the original work, we use elementary inequalities for metric spaces and embeddings in Hilbert spaces.