Testing for independence in arbitrary distributions. (7th January 2019)

• Record Type: Journal Article
• Authors: Genest, C; Nešlehová, J G; Rémillard, B; Murphy, O A
• Is Part Of: Biometrika. Volume 106:Number 1(2019:Mar.)
• Page Start: 47
• Page End: 68
• Publication Date: 2019-01-07
• Subjects: Independence test -- Mixed data -- Multilinear copula -- Sparse contingency table -- Wild bootstrap; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asy059
• Languages: English
• ISSNs: 0006-3444

Abstract

SUMMARY: 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 Cramér–von Mises type whose asymptotic behaviour derives from the empirical multilinear copula process. Approximate $p$ -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.