Rank Tests for Elliptical Graphical Modeling

Davy Paindaveine and Thomas Verdebout

Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: As a reaction to the restrictive Gaussian assumptions that are usually part of graphical models, Vogel and Fried [17] 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.

Keywords: conditional independence; graphical models; local symptotic normality; psuedo-gaussian tests; rank tests; scatter matrix; signed ranks (search for similar items in EconPapers)
Pages: 19 p.
Date: 2011-12
New Economics Papers: this item is included in nep-ecm
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