Independent Quadratic Forms in 3-Variance-Component Models

Abstract

This article addresses derivation and existence of quadratic forms that were suggested by Burch (2007) for procedures for inference on variance components in mixed linear models in combination with generalized fiducial inference. A relatively simple algorithm leading to the required quadratic forms in a general 3-variance-component model is stated and designs for two-way ANOVA models without interactions that permit Burch's procedure are characterized. This complements developments in the original article by Burch.

Keywords:

• Independent quadratic forms
• Random effects
• Two-way ANOVA without interactions
• Variance components

Mathematics Subject Classification:

• 62J10
• 62F99

Acknowledgment

The author would like to thank an anonymous reviewer for insightful comments and suggestions that improved presentation of this article.