Economics at your fingertips  

Semiparametrically Efficient Tests of Multivariate Independence Using Center-Outward Quadrant, Spearman, and Kendall Statistics

Hongjian Shi, Mathias Drton, Marc Hallin and Fang Han

No 2023-03, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: Defining multivariate generalizations of the classical univariate ranks has been a long-standing open problem in statistics. Optimal transport has been shown to offer a solution in which multivariate ranks are obtained by transporting data points to a grid that approximates a uniformreference measure (Chernozhukov et al. 2017; Hallin, 2017; Hallin et al. 2021). We take up this new perspective to develop and study multivariate analogues of the sign covariance/quadrant statistic, Kendall’s tau, and Spearman’s rho. The resulting tests of multivariate independence are genuinely distribution-free, hence uniformly valid irrespective of the actual (absolutely continuous) distributions of the observations. Our results provide asymptotic distribution theory for these new test statistics, with asymptotic approximations to critical values to be used for testing independence as well as a power analysis of the resulting tests. This includes a multivariate elliptical Chernoff–Savage property, which guarantees that, under ellipticity, our nonparametric tests of independence enjoy an asymptotic relative efficiency of one or larger with respect to theclassical Gaussian procedures.

Keywords: Semiparametrically Efficient Tests; Multivariate Independence; Center-Outward Quadrant; Spearman; Kendall Statistics (search for similar items in EconPapers)
Pages: 36 p.
Date: 2023-01
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc

Published by:

Downloads: (external link) ... DRTON_HALLIN_HAN.pdf Œuvre complète ou partie de l'œuvre (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This working paper can be ordered from ...

Access Statistics for this paper

More papers in Working Papers ECARES from ULB -- Universite Libre de Bruxelles Contact information at EDIRC.
Bibliographic data for series maintained by Benoit Pauwels ().

Page updated 2024-04-19
Handle: RePEc:eca:wpaper:2013/355918