On the Finite-Sample Performance of Measure-Transportation-Based Multivariate Rank Tests

Marc Hallin and Gilles Mordant
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Gilles Mordant: Universität Göttingen, IMS

A chapter in Robust and Multivariate Statistical Methods, 2023, pp 87-119 from Springer

Abstract: Abstract Extending to dimension two and higher the dual univariate concepts of ranks and quantiles has remained an open problem for more than half a century. Based on measure transportation results, a solution has been proposed recently under the name center-outward ranks and quantiles. Contrary to previous proposals, center-outward ranks enjoy all the properties that make univariate ranks a successful tool for statistical inference. Just as their univariate counterparts (to which they reduce in dimension one), they allow for the construction of distribution-free and asymptotically efficient tests for a variety of problems where the density of some underlying noise or innovation remains unspecified. The actual implementation of these tests involves the somewhat arbitrary choice of a grid. While the asymptotic impact of that choice is nil, its finite-sample consequences are not. In this note, we investigate this finite-sample impact in the typical context of the multivariate two-sample location problem.

Keywords: Measure transportation; Multivariate ranks; Two-sample rank tests (search for similar items in EconPapers)
Date: 2023
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Working Paper: On the finite-sample performance of measure-transportation-based multivariate rank tests (2023)
Working Paper: On the Finite-Sample Performance of Measure Transportation-Based Multivariate Rank Tests (2021)
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DOI: 10.1007/978-3-031-22687-8_5

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