Numerical Study of Small Sample Variances of Estimators of Variance Components in the Two-Way Factorial Model

Abstract

Many estimation procedures have been proposed for estimating variance components in unbalanced factorial models. A large proportion of these are based on the solution to a system of linear equations obtained from a set of quadratic forms and their expected value. This paper will present a numerical study of the small sample variance of eight variance component estimators of this type. The variances will be compared to the Bhattacharyya lower bound for unbiased estimators.

Keywords:

• variance components
• quadratic forms
• ANOVA estimates
• MINQUE estimates
• average estimates
• Bhattacharyya lower bound