Symmetric rank covariances: a generalized framework for nonparametric measures of dependence

• 成果类型: Article
• 署名作者: Weihs, L.; Drton, M.; Meinshausen, N.
• 署名单位: University of Washington; University of Washington Seattle; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy021
• 发表日期: 2018
• 页码: 547562
• 关键词: INDEPENDENCE; association

摘要

The need to test whether two random vectors are independent has spawned many competing measures of dependence. We focus on nonparametric measures that are invariant under strictly increasing transformations, such as Kendall's tau, Hoeffding's D, and the Bergsma-Dassios sign covariance. Each exhibits symmetries that are not readily apparent from their definitions. Making these symmetries explicit, we define a new class of multivariate nonparametric measures of dependence that we call symmetric rank covariances. This new class generalizes the above measures and leads naturally to multivariate extensions of the Bergsma-Dassios sign covariance. Symmetric rank covariances may be estimated unbiasedly using U-statistics, for which we prove results on computational efficiency and large-sample behaviour. The algorithms we develop for their computation include, to the best of our knowledge, the first efficient algorithms for Hoeffding's D statistic in the multivariate setting.