Elliptical graphical modelling

Daniel Vogel, Roland Fried

Research output: Contribution to journalArticle

14 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)935-951
Number of pages17
JournalBiometrika
Volume98
Issue number4
Early online date13 Oct 2011
DOIs
Publication statusPublished - Dec 2011

Fingerprint

Graphical Modeling
Demography
Partial Correlation
Deviance
Estimator
Graphical Models
Scatter
Population distribution
Heavy Tails
Chi-square
Distribution-free
Asymptotic Variance
Gaussian Model
Decomposable
Equivariant
Test Statistic
population distribution
Statistics
Simulation Study
Model-based

Cite this

Elliptical graphical modelling. / Vogel, Daniel; Fried, Roland .

In: Biometrika, Vol. 98, No. 4, 12.2011, p. 935-951.

Research output: Contribution to journalArticle

Vogel, Daniel ; Fried, Roland . / Elliptical graphical modelling. In: Biometrika. 2011 ; Vol. 98, No. 4. pp. 935-951.
@article{75eff77b6d0c4f63b2b9df90182a1d8d,
title = "Elliptical graphical modelling",
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.",
author = "Daniel Vogel and Roland Fried",
year = "2011",
month = "12",
doi = "10.1093/biomet/asr037",
language = "English",
volume = "98",
pages = "935--951",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",
number = "4",

}

TY - JOUR

T1 - Elliptical graphical modelling

AU - Vogel, Daniel

AU - Fried, Roland

PY - 2011/12

Y1 - 2011/12

N2 - 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.

AB - 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.

U2 - 10.1093/biomet/asr037

DO - 10.1093/biomet/asr037

M3 - Article

VL - 98

SP - 935

EP - 951

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 4

ER -