Maximum likelihood estimation of a set of covariance matrices under Löwner order restrictions with applications to balanced multivariate variance components models (Q1175387)

The problem of variance component estimation in univariate mixed models has been studied by many authors. They proposed the moment estimation, procedures for maximum likelihood, restricted maximum likelihood (REML) estimation, MINQU and MIVQU estimators. In this paper, the authors consider the problem in the multivariate case by using the maximum likelihood estimation under Löwner order restrictions. They show that a dual formulation of the problem is useful. Due to the relationship between the primal and dual problems the authors suggest a general algorithm. Some applications of the algorithm in balanced multivariate variance components models are given. A discussion on the speed of convergence for variance components is also given.