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On the finite-sample performance of measure-transportation-based multivariate rank tests

Author

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  • Marc Hallin
  • Gilles Mordant

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.

Suggested Citation

  • Marc Hallin & Gilles Mordant, 2023. "On the finite-sample performance of measure-transportation-based multivariate rank tests," ULB Institutional Repository 2013/376174, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/376174
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