Optimal rank-based tests for homogeneity of scatter
The Annals of Statistics · 2008 · Volume 36 · Issue 3
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.
Keywords
62G35, 62M15, Adaptivity, Elliptic densities, local asymptotic normality, scatter matrix, Semiparametric efficiency, shape matrix
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