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December 2008 Flexible covariance estimation in graphical Gaussian models
Bala Rajaratnam, Hélène Massam, Carlos M. Carvalho
Ann. Statist. 36(6): 2818-2849 (December 2008). DOI: 10.1214/08-AOS619

Abstract

In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the WPG family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278–1323] we derive closed-form expressions for Bayes estimators under the entropy and squared-error losses. The WPG family includes the classical inverse of the hyper inverse Wishart but has many more shape parameters, thus allowing for flexibility in differentially shrinking various parts of the covariance matrix. Moreover, using this family avoids recourse to MCMC, often infeasible in high-dimensional problems. We illustrate the performance of our estimators through a collection of numerical examples where we explore frequentist risk properties and the efficacy of graphs in the estimation of high-dimensional covariance structures.

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Bala Rajaratnam. Hélène Massam. Carlos M. Carvalho. "Flexible covariance estimation in graphical Gaussian models." Ann. Statist. 36 (6) 2818 - 2849, December 2008. https://doi.org/10.1214/08-AOS619

Information

Published: December 2008
First available in Project Euclid: 5 January 2009

zbMATH: 1168.62054
MathSciNet: MR2485014
Digital Object Identifier: 10.1214/08-AOS619

Subjects:
Primary: 62C10 , 62F15 , 62H12

Keywords: Bayes estimators , Covariance estimation , Gaussian graphical models , regularization , shrinkage

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 6 • December 2008
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