 On the finite-sample performance of measure-transportation-based multivariate rank testsMarc Hallin and Gilles Mordant ULB Institutional Repository from ULB -- Universite Libre de Bruxelles 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) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:ulb:ulbeco:2013/376174 Ordering information: This working paper can be ordered from Access Statistics for this paper More papers in ULB Institutional Repository from ULB -- Universite Libre de Bruxelles Contact information at EDIRC. |
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