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Hallin, Marc; Paindaveine, Davy

Optimal rank-based tests for homogeneity of scatter. (English) Zbl 1360.62288

Ann. Stat. 36, No. 3, 1261-1298 (2008).
Summary: 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.

Cited in 12 Documents

MSC:

62H15 Hypothesis testing in multivariate analysis
62G10 Nonparametric hypothesis testing
62G35 Nonparametric robustness

Keywords:

elliptic densities; scatter matrix; shape matrix; local asymptotic normality; semiparametric efficiency; adaptivity
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References:

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