The Annals of Statistics

Maximum Likelihood Estimators and Likelihood Ratio Criteria in Multivariate Components of Variance

Blair M. Anderson, T. W. Anderson, and Ingram Olkin

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Abstract

Maximum likelihood estimators are obtained for multivariate components of variance models under the condition that the effect covariance matrix is positive semidefinite with a maximum rank. The rank of the estimator is random. The estimation procedure leads to a likelihood ratio test that the rank of the effect matrix is not greater than a given number against the alternative that the rank is not greater than a larger specified number. Linear structural relationship models and some factor analytic models can be put into this framework.

Article information

Source
Ann. Statist., Volume 14, Number 2 (1986), 405-417.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349929

Digital Object Identifier
doi:10.1214/aos/1176349929

Mathematical Reviews number (MathSciNet)
MR840505

Zentralblatt MATH identifier
0631.62063

JSTOR
links.jstor.org

Subjects
Primary: 62H12: Estimation
Secondary: 62J10: Analysis of variance and covariance

Keywords
Multivariate analysis of variance linear structural models factor analysis models

Citation

Anderson, Blair M.; Anderson, T. W.; Olkin, Ingram. Maximum Likelihood Estimators and Likelihood Ratio Criteria in Multivariate Components of Variance. Ann. Statist. 14 (1986), no. 2, 405--417. doi:10.1214/aos/1176349929. https://projecteuclid.org/euclid.aos/1176349929


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