Asymptotic local efficiency of Cram\'{e}r--von Mises tests for multivariate independence
Abstract
Deheuvels [J. Multivariate Anal. 11 (1981) 102--113] and Genest and R\'{e}millard [Test 13 (2004) 335--369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cram\'{e}r--von Mises statistics derived from a M\"{o}bius decomposition of the empirical copula process. A result on the large-sample behavior of this process under contiguous sequences of alternatives is used here to give a representation of the limiting distribution of such test statistics and to compute their relative local asymptotic efficiency. Local power curves and asymptotic relative efficiencies are compared under familiar classes of copula alternatives.
Cite
@article{arxiv.0708.0485,
title = {Asymptotic local efficiency of Cram\'{e}r--von Mises tests for multivariate independence},
author = {Christian Genest and Jean-François Quessy and Bruno Rémillard},
journal= {arXiv preprint arXiv:0708.0485},
year = {2009}
}
Comments
Published at http://dx.doi.org/10.1214/009053606000000984 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)