Optimal rank-based tests for homogeneity of scatter
Marc Hallin and Davy Paindaveine
Source: Ann. Statist. Volume 36, Number 3
(2008), 1261-1298.
Abstract
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.
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Keywords: Elliptic densities; scatter matrix; shape matrix; local asymptotic normality; semiparametric efficiency; adaptivity
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1211819564
Digital Object Identifier: doi:10.1214/07-AOS508
Mathematical Reviews number (MathSciNet): MR2418657
Zentralblatt MATH identifier: 05294973
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