Distribution-free estimators of variance components for multivariate linear mixed models

Abstract

Non-iterative, distribution-free, and unbiased estimators of variance components including minimum norm quadratic unbiased estimators and the method of moments estimators are derived for multivariate linear mixed models. 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. Some properties of the proposed estimators such as unbiasedness and existence are discussed, and related computational issues are addressed. A simulation study is conducted to compare the proposed estimators with Gaussian (restricted) maximum likelihood estimators in terms of bias and mean square error. An application of gene expression family study is presented to illustrate the proposed estimators.