Testing for independence in arbitrary distributions

• 成果类型: Article
• 署名作者: Genest, C.; Neslehova, J. G.; Remillard, B.; Murphy, O. A.
• 署名单位: McGill University; Universite de Montreal; HEC Montreal
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy059
• 发表日期: 2019
• 页码: 4768
• 关键词: multivariate nonparametric test; multilinear copula process; local efficiency

摘要

Statistics are proposed for testing the hypothesis that arbitrary random variables are mutually independent. The tests are consistent and well behaved for any marginal distributions; they can be used, for example, for contingency tables which are sparse or whose dimension depends on the sample size, as well as for mixed data. No regularity conditions, data jittering, or binning mechanisms are required. The statistics are rank-based functionals of Cramer-von Mises type whose asymptotic behaviour derives from the empirical multilinear copula process. Approximate -values are computed using a wild bootstrap. The procedures are simple to implement and computationally efficient, and maintain their level well in moderate to large samples. Simulations suggest that the tests are robust with respect to the number of ties in the data, can easily detect a broad range of alternatives, and outperform existing procedures in many settings. Additional insight into their performance is provided through asymptotic local power calculations under contiguous alternatives. The procedures are illustrated on traumatic brain injury data.