Maximum likelihood estimators and likelihood ratio criteria in multivariate components of variance. (English) Zbl 0631.62063

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

Ann. Stat. 14, 405-417 (1986).

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.

MSC:

62H12	Estimation in multivariate analysis
62J10	Analysis of variance and covariance (ANOVA)

Keywords:

Maximum likelihood estimators; multivariate components of variance models; effect covariance matrix; positive semidefinite; maximum rank; likelihood ratio test; Linear structural relationship models; factor analytic models