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June 2008 Optimal rank-based tests for homogeneity of scatter
Marc Hallin, Davy Paindaveine
Ann. Statist. 36(3): 1261-1298 (June 2008). DOI: 10.1214/07-AOS508


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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Marc Hallin. Davy Paindaveine. "Optimal rank-based tests for homogeneity of scatter." Ann. Statist. 36 (3) 1261 - 1298, June 2008.


Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1360.62288
MathSciNet: MR2418657
Digital Object Identifier: 10.1214/07-AOS508

Primary: 62G35 , 62M15

Keywords: Adaptivity , Elliptic densities , local asymptotic normality , scatter matrix , Semiparametric efficiency , shape matrix

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 3 • June 2008
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