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Activity Number: 306 - Algorithmic and Inferential Advances in Univariate and Multivariate Tuning-Parameter-Free Nonparametric Procedures
Type: Topic Contributed
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
Sponsor: Section on Statistical Learning and Data Science
Abstract #309627
Title: Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation
Author(s): Bodhisattva Sen* and Nabarun Deb
Companies: Columbia University and Columbia University
Keywords: goodness-of-fit testing; optimal tranport; testing for independence

In this talk we propose a general framework for distribution-free nonparametric testing in multi-dimensions, based on a notion of multivariate ranks which are defined using the theory of measure transportation. Unlike other existing proposals in the literature, these multivariate ranks share a number of similar properties with the usual notion of one-dimensional ranks; most importantly, these ranks are distribution-free. This crucial observation allows us to design nonparametric tests which are based on statistics that are exactly distribution-free under the null hypothesis. We illustrate the applicability of this approach by constructing exact distribution-free tests for two classical nonparametric problems: (i) testing for mutual independence between random vectors, and, (ii) testing for the equality of multivariate distributions. In both these problems we derive the asymptotic null distribution of the proposed statistic. We further show that our tests are consistent against very general alternatives. Moreover, the proposed tests are tuning-free, computationally feasible and are well-defined under minimal assumptions on the underlying distributions.

Authors who are presenting talks have a * after their name.

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