Minimum variance unbiased invariant estimation of variance components under normality

Abstract

In a variance components model for normally distributed data, for a specified vector of linear combinations of the variance components, necessary and sufficient conditions are given under which the vector has a uniformly minimum variance unbiased translation-invariant estimator. The competing class of estimators is not restricted to those that are quadratic. For classification models, the conditions are translated into easy-to-check partial balance requirements on the incidence array.

Keywords:

• Best unbiased estimator
• MINQUE
• Cramer-Rao lower bound
• Quadratic subspace
• Mixed-effects linear model
• Classification model
• ANOVA model