par Hallin, Marc 
;Mordant, Gilles
Référence Robust and Multivariate Statistical Methods: Festschrift in Honor of David E. Tyler, Springer International Publishing, page (87-119)
Publication Publié, 2023-04
;Mordant, GillesRéférence Robust and Multivariate Statistical Methods: Festschrift in Honor of David E. Tyler, Springer International Publishing, page (87-119)
Publication Publié, 2023-04
Partie d'ouvrage collectif
| Résumé : | 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. |
