Measuring and testing dependence by correlation of distances
成果类型：
Article
署名作者：
Szekely, Gabor J.; Rizzo, Maria L.; Bakirov, Nail K.
署名单位：
University System of Ohio; Bowling Green State University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; Russian Academy of Sciences
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053607000000505
发表日期：
2007
页码：
2769-2794
关键词：
摘要：
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are discussed. Implementation of the test and Monte Carlo results are also presented.