Estimation of means in graphical Gaussian models with symmetries

TL;DR

This paper investigates conditions under which the maximum likelihood and least-squares estimators of means are equal in symmetric graphical Gaussian models, providing a complete characterization of estimability based on variable partitions.

Contribution

It offers a necessary and sufficient condition for mean estimability in symmetric graphical Gaussian models, extending previous research.

Findings

Derived a complete criterion for estimator equality

Characterized partitions ensuring estimability

Enhanced understanding of symmetry constraints in Gaussian models

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.