Elliptical graphical modelling

Abstract

We propose elliptical graphical models based on conditional uncorrelatedness as a general- ization of Gaussian graphical models by letting the population distribution be elliptical instead of normal, allowing the fitting of data with arbitrarily heavy tails. We study the class of propor- tionally affine equivariant scatter estimators and show how they can be used to perform elliptical graphical modelling, leading to a new class of partial correlation estimators and analogues of the classical deviance test. General expressions for the asymptotic variance of partial correla- tion estimators, unconstrained and under decomposable models, are given, and the asymptotic chi square approximation of 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. Our approach provides a robustification of Gaussian graphical modelling. The latter is likelihood-based and known to be very sensitive to model misspecification and outlying observations.

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• Rejoinder to "Breakdown and groups" by P. L. Davies and U. Gather
• Breakdown and groups
• Discussion of "Breakdown and groups" by P. L. Davies and U. Gather
• Discussion of "Breakdown and groups" by P. L. Davies and U. Gather
• Discussion of "Breakdown and groups" by P. L. Davies and U. Gather
• Discussion of "Breakdown and groups" by P. L. Davies and U. Gather
• Discussion of "Breakdown and groups" by P. L. Davies and U. Gather
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• Semiparametrically efficient rank-based inference for shape II. Optimal R-estimation of shape

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• Large Covariance Estimation through Elliptical Factor Models
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• A review of Gaussian Markov models for conditional independence
• Robust estimators for non-decomposable elliptical graphical models
• Asymptotics of the two-stage spatial sign correlation
• Computing the Oja Median in R: The Package OjaNP
• Selection and Estimation for Mixed Graphical Models
• Groups acting on Gaussian graphical models
• Non-Independent Components Analysis
• A nonparametric test for elliptical distribution based on kernel embedding of probabilities
• Predictive Learning on Hidden Tree-Structured Ising Models
• Elliptical Symmetry Tests in \proglang{R}
• Combining Smoothing Spline with Conditional Gaussian Graphical Model for Density and Graph Estimation