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Elliptical graphical modelling

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  • D. Vogel
  • R. Fried

Abstract

We propose elliptical graphical models based on conditional uncorrelatedness as a robust generalization of Gaussian graphical models. Letting the population distribution be elliptical instead of normal allows the fitting of data with arbitrarily heavy tails. We study the class of proportionally affine equivariant scatter estimators and show how they can be used to perform elliptical graphical modelling. This leads to a new class of partial correlation estimators and analogues of the classical deviance test. General expressions for the asymptotic variance of partial correlation estimators, unconstrained and under decomposable models, are given, and the asymptotic chi square approximation for the pseudo-deviance test statistic is proved. The feasibility of our approach is demonstrated by a simulation study, using, among others, Tyler's scatter estimator, which is distribution-free within the elliptical model. Copyright 2011, Oxford University Press.

Suggested Citation

  • D. Vogel & R. Fried, 2011. "Elliptical graphical modelling," Biometrika, Biometrika Trust, vol. 98(4), pages 935-951.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:4:p:935-951
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    File URL: http://hdl.handle.net/10.1093/biomet/asr037
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    Cited by:

    1. Vinciotti, Veronica & Hashem, Hussein, 2013. "Robust methods for inferring sparse network structures," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 84-94.
    2. Sladana Babic & Laetitia Gelbgras & Marc Hallin & Christophe Ley, 2019. "Optimal tests for elliptical symmetry: specified and unspecified location," Working Papers ECARES 2019-26, ULB -- Universite Libre de Bruxelles.
    3. Dürre, Alexander & Vogel, Daniel, 2016. "Asymptotics of the two-stage spatial sign correlation," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 54-67.
    4. Davy Paindaveine & Thomas Verdebout, 2011. "Rank Tests for Elliptical Graphical Modeling," Working Papers ECARES ECARES 2011-039, ULB -- Universite Libre de Bruxelles.
    5. Daniel Felix Ahelegbey, 2015. "The Econometrics of Networks: A Review," Working Papers 2015:13, Department of Economics, University of Venice "Ca' Foscari".

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