The Annals of Statistics

Symmetry and lattice conditional independence in a multivariate normal distribution

Steen Andersson and Jesper Madsen

Full-text: Open access

Abstract

A class of multivariate normal models with symmetry restrictions given by a finite group and conditional independence restrictions given by a finite distributive lattice is defined and studied. The statistical properties of these models including maximum likelihood inference, invariance and hypothesis testing are discussed.

Article information

Source
Ann. Statist., Volume 26, Number 2 (1998), 525-572.

Dates
First available in Project Euclid: 31 July 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1028144848

Digital Object Identifier
doi:10.1214/aos/1028144848

Mathematical Reviews number (MathSciNet)
MR1626059

Zentralblatt MATH identifier
0943.62047

Subjects
Primary: 62H12: Estimation 62H15: Hypothesis testing
Secondary: 62H10: Distribution of statistics 62H20: Measures of association (correlation, canonical correlation, etc.) 62A05

Keywords
Group symmetry invariance orthogonal group representation quotient space conditional independence distributive lattice join-irreducible elements maximum likelihood estimator likelihood ratio test multivariate normal distribution

Citation

Andersson, Steen; Madsen, Jesper. Symmetry and lattice conditional independence in a multivariate normal distribution. Ann. Statist. 26 (1998), no. 2, 525--572. doi:10.1214/aos/1028144848. https://projecteuclid.org/euclid.aos/1028144848


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References

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  • BLOOMINGTON, INDIANA 47405 E-MAIL: standers@ucs.indiana.edu jmadsen@math.ku.dk