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April 2012 Estimation of means in graphical Gaussian models with symmetries
Helene Gehrmann, Steffen L. Lauritzen
Ann. Statist. 40(2): 1061-1073 (April 2012). DOI: 10.1214/12-AOS991


We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose corresponding means are restricted to being identical. We find a necessary and sufficient condition on the partition to ensure equality between the maximum likelihood and least-squares estimators of the mean.


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Helene Gehrmann. Steffen L. Lauritzen. "Estimation of means in graphical Gaussian models with symmetries." Ann. Statist. 40 (2) 1061 - 1073, April 2012.


Published: April 2012
First available in Project Euclid: 18 July 2012

zbMATH: 1274.62366
MathSciNet: MR2985943
Digital Object Identifier: 10.1214/12-AOS991

Primary: 62H12
Secondary: 62F99

Keywords: Conditional independence , Invariance , maximum likelihood estimation , patterned mean vector , symmetry

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 2 • April 2012
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