Estimation of Sampling (Co)variances of the REML Estimators for Variance Components in a Mixed Linear Model.

Abstract

We derive an expression of sampling (co) variances of the restricted maximum likelihood estimators of variance components in a mixed linear model with one random effect except for the residual term. The given matrix describing the sampling (co) variances is not a log likelihood-based one, but is rather developed noticing the equivalence between the restricted maximum likelihood estimators and the corresponding estimators by a minimum variance quadratic unbiased estimation in which the prior information for the variance ratio is based on the restricted maximum likelihood estimators of variance components. The current approach takes account of the exact (co) variances of the quadratics for the minimum variance quadratic unbiased estimation under normality, and the matrix derived is different from the inverse of the so-called information matrix which represents the large-sample, asymptotic dispersion matrix of the restricted maximum likelihood estimators. A numerical comparison is conducted to confirm the validity of our approach.