DISTANCE MULTIVARIANCE: NEW DEPENDENCE MEASURES FOR RANDOM VECTORS

• 成果类型: Article
• 署名作者: Boettcher, Bjoern; Keller-Ressel, Martin; Schilling, Rene L.
• 署名单位: Technische Universitat Dresden
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1764
• 发表日期: 2019
• 页码: 2757-2789
• 关键词: INDEPENDENCE; covariance

摘要

We introduce two new measures for the dependence of n >= 2 random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted L-2-distance of quantities related to the characteristic functions of the underlying random variables. These extend distance covariance (introduced by Szekely, Rizzo and Bakirov) from pairs of random variables to n-tuplets of random variables. We show that total distance multivariance can be used to detect the independence of n random variables and has a simple finite-sample representation in terms of distance matrices of the sample points, where distance is measured by a continuous negative definite function. Under some mild moment conditions, this leads to a test for independence of multiple random vectors which is consistent against all alternatives.