Using the Sinkhorn divergence in permutation tests for the multivariate two-sample problem

TL;DR

This paper introduces a computationally feasible permutation test for the multivariate two-sample problem using Sinkhorn divergence, comparing its performance with existing non-parametric tests through simulations.

Contribution

It proposes a novel permutation testing method based on Sinkhorn divergence tailored for large sample multivariate data, with analysis of its asymptotic distribution.

Findings

The Sinkhorn-based test performs competitively with Schilling's test in simulations.

Different implementation strategies for the test are evaluated.

Asymptotic distribution results are established for some test variants.

Abstract

In order to adapt the Wasserstein distance to the large sample multivariate non-parametric two-sample problem, making its application computationally feasible, permutation tests based on the Sinkhorn divergence between probability vectors associated to data dependent partitions are considered. Different ways of implementing these tests are evaluated and the asymptotic distribution of the underlying statistic is established in some cases. The statistics proposed are compared, in simulated examples, with the test of Schilling's, one of the best non-parametric tests available in the literature.