Multivariate tests of association based on univariate tests

Ruth Heller, Yair Heller

Research output: Contribution to journalConference articlepeer-review

Abstract

For testing two vector random variables for independence, we propose testing whether the distance of one vector from an arbitrary center point is independent from the distance of the other vector from another arbitrary center point by a univariate test. We prove that under minimal assumptions, it is enough to have a consistent univariate independence test on the distances, to guarantee that the power to detect dependence between the random vectors increases to one with sample size. If the univariate test is distribution-free, the multivariate test will also be distribution-free. If we consider multiple center points and aggregate the center-specific univariate tests, the power may be further improved, and the resulting multivariate test may have a distribution-free critical value for specific aggregation methods (if the univariate test is distribution free). We show that certain multivariate tests recently proposed in the literature can be viewed as instances of this general approach. Moreover, we show in experiments that novel tests constructed using our approach can have better power and computational time than competing approaches.

Original languageEnglish
Pages (from-to)208-216
Number of pages9
JournalAdvances in Neural Information Processing Systems
StatePublished - 2016
Event30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain
Duration: 5 Dec 201610 Dec 2016

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