Estimation of means in graphical Gaussian models with symmetries
Helene Gehrmann, Steffen L. Lauritzen
The Annals of Statistics · 2012 · Volume 40 · Issue 2
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.
Keywords
62F99, 62H12, Conditional independence, Invariance, maximum likelihood estimation, patterned mean vector, symmetry
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