ESTIMATION OF MEANS IN GRAPHICAL GAUSSIAN MODELS WITH SYMMETRIES

ESTIMATION OF MEANS IN GRAPHICAL GAUSSIAN MODELS WITH SYMMETRIES

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...

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Veröffentlicht in:The Annals of statistics 2012-04, Vol.40 (2), p.1061-1073
Hauptverfasser: Gehrmann, Helene, Lauritzen, Steffen L.
Format: Artikel
Sprache:eng
Schlagworte:
62F99
62H12
Conditional independence
Covariance
Estimating techniques
Estimators
invariance
Least squares
Mathematical vectors
Maximum likelihood estimation
Maximum likelihood estimators
Normal distribution
patterned mean vector
Statistics
Studies
Sufficient conditions
Symmetry
Vertices
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Beschreibung
Zusammenfassung: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/12-AOS991