Rank Tests for Elliptical Graphical Modeling
As a reaction to the restrictive Gaussian assumptions that are usually part of graphical models, Vogel and Fried  recently introduced elliptical graphical models, in which the vector of variables at hand is assumed to have an elliptical distribution. The present work introduces a class of rank tests in the context of elliptical graphical models. The proposed tests are valid under any elliptical density, and in particular do not require any moment assumption. They achieve local and asymptotic optimality under correctly specified densities. Their asymptotic properties are investigated both under the null and under sequences of local alternatives. Asymptotic relative efficiencies with respect to the corresponding pseudo-Gaussian competitors are derived, which allows to show that, when based on normal scores, the proposed rank tests uniformly dominate the pseudo-Gaussian tests in the Pitman sense. The asymptotic results are confirmed through a Monte-Carlo study.
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- Paindaveine, Davy, 2006. "A Chernoff-Savage result for shape:On the non-admissibility of pseudo-Gaussian methods," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2206-2220, November.
- Marc Hallin & Davy Paindaveine & Thomas Verdebout, 2009. "Optimal rank-based testing for principal component," Working Papers ECARES 2009_013, ULB -- Universite Libre de Bruxelles.
- Sirkku Pauliina Ilmonen & Davy Paindaveine, 2011. "Semiparametrically Efficient Inference Based on Signed Ranks in Symmetric Independent Component Models," Working Papers ECARES ECARES 2011-003, ULB -- Universite Libre de Bruxelles.
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