Some asymptotic properties of constrained generalized least squares estimation in coy ariance structure models

Abstract

Some basic results by Browne (1974) on generalized least squares estimation in the analysis of covariance structures are extended to covariance structures with parameters subject to arbitrary nonlinear constraints. It is shown that the constrained estimators are consistent, asymptotically multivariate normally distributed, and asymptotically equivalent to constrained maximum likelihood estimators. Asymptotic chi-square tests are developed to evaluate appropriate model comparisons. The relationships between the Lagrangian approach and the reparameterization approach are discussed.