The Annals of Statistics

Estimation of means in graphical Gaussian models with symmetries

Helene Gehrmann and Steffen L. Lauritzen

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Abstract

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.

Article information

Source
Ann. Statist. Volume 40, Number 2 (2012), 1061-1073.

Dates
First available in Project Euclid: 18 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1342625461

Digital Object Identifier
doi:10.1214/12-AOS991

Mathematical Reviews number (MathSciNet)
MR2985943

Zentralblatt MATH identifier
1274.62366

Subjects
Primary: 62H12: Estimation
Secondary: 62F99: None of the above, but in this section

Keywords
Conditional independence invariance maximum likelihood estimation patterned mean vector symmetry

Citation

Gehrmann, Helene; Lauritzen, Steffen L. Estimation of means in graphical Gaussian models with symmetries. Ann. Statist. 40 (2012), no. 2, 1061--1073. doi:10.1214/12-AOS991. https://projecteuclid.org/euclid.aos/1342625461.


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