MIVQUE and REML Estimators of Variance Components under Proportionality Condition

Abstract

In this study, a one-way random effect model with unequal cell variances is considered, and the Minimum Variance Quadratic Unbiased Estimator (MIVQUE) and Restricted Maximum Likelihood (REML) estimator of the variance components are studied. The algebraic inversion of the variance matrix of the observation vector is obtained to achieve some computational convenience. Using the proportionality condition described by Talukder (1992) that the cell sizes are proportional to the cell variances, MIVQUE and REML estimators are shown to be the same as the ANOVA estimators.