Variance least squares estimators for multivariate linear mixed model

Non-iterative, distribution-free, and unbiased estimators of variance components by least squares method are derived for multivariate linear mixed model. A general inter-cluster variance matrix, a same-member only general inter-response variance matrix, and an uncorrelated intra-cluster error structure for each response are assumed. Projection method is suggested when unbiased estimators of variance components are not nonnegative definite matrices. A simulation study is conducted to investigate the properties of the proposed estimators in terms of bias and mean square error with comparison to the Gaussian (restricted) maximum likelihood estimators. The proposed estimators are illustrated by an application of gene expression familial study.