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

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.]