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

Marc Hallin and Gilles Mordant

No 2021-24, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: Extending to dimension 2 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 which, contrary to previous proposals, enjoys 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), center-outward ranks allow for the construction of distribution-free and asymptotically efficient tests for a variety of problemswhere the density of some noise or innovation remains unspecified. The actual implementation of these testsinvolves 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 the finite-sample impact of that choice in the typical context of the multivariate two-sample location problem.

Keywords: Ranks; Time series; Frequency domain; Time-reversibility (search for similar items in EconPapers)
Pages: 24 p.
Date: 2021-11
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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