Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs

• 成果类型: Article
• 署名作者: Shi, Hongjian; Drton, Mathias; Han, Fang
• 署名单位: University of Washington; University of Washington Seattle; Technical University of Munich
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1782223
• 发表日期: 2022
• 页码: 395-410
• 关键词: CENTRAL-LIMIT-THEOREM; Asymptotic Normality; distance correlation; association; dependence; INFORMATION; Connection; covariance; statistics; algorithms

摘要

This article investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the center-outward ranks and signs developed by Marc Hallin and collaborators. In technical terms, the proposed test is consistent and distribution-free in the family of multivariate distributions with nonvanishing (Lebesgue) probability densities. Exploiting the (degenerate) U-statistic structure of the distance covariance and the combinatorial nature of Hallin's center-outward ranks and signs, we are able to derive the limiting null distribution of our test statistic. The resulting asymptotic approximation is accurate already for moderate sample sizes and makes the test implementable without requiring permutation. The limiting distribution is derived via a more general result that gives a new type of combinatorial noncentral limit theorem for double- and multiple-indexed permutation statistics. Supplementary materials for this article are available online.