%0 Journal Article
%T Optimal rank-based tests for homogeneity of scatter
%A Marc Hallin
%A Davy Paindaveine
%J Mathematics
%D 2008
%I arXiv
%R 10.1214/07-AOS508
%X We propose a class of locally and asymptotically optimal tests, based on multivariate ranks and signs for the homogeneity of scatter matrices in $m$ elliptical populations. Contrary to the existing parametric procedures, these tests remain valid without any moment assumptions, and thus are perfectly robust against heavy-tailed distributions (validity robustness). Nevertheless, they reach semiparametric efficiency bounds at correctly specified elliptical densities and maintain high powers under all (efficiency robustness). In particular, their normal-score version outperforms traditional Gaussian likelihood ratio tests and their pseudo-Gaussian robustifications under a very broad range of non-Gaussian densities including, for instance, all multivariate Student and power-exponential distributions.
%U http://arxiv.org/abs/0806.2963v1