Elliptical graphical modelling

• Published in: Biometrika Vol. 98; no. 4; pp. 935 - 951
• Main Authors: Fried, R, Vogel, D
• Format: Journal Article
• Language: English
• Published: Oxford University Press for Biometrika Trust 01.12.2011
• Series: Biometrika
• ISSN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asr037

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.