Estimation of means in graphical Gaussian models with symmetries

Helene Gehrmann; Steffen L. Lauritzen

doi:10.1214/12-AOS991

Estimation of means in graphical Gaussian models with symmetries

2 Citations (Scopus)

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.

Original language	English
Journal	Annals of Statistics
Volume	40
Issue number	2
Pages (from-to)	1061-1073
Number of pages	13
ISSN	0090-5364
DOIs	https://doi.org/10.1214/12-AOS991
Publication status	Published - Apr 2012
Externally published	Yes

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10.1214/12-AOS991

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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.",

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AB - 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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