Confidence Regions for Variance Components in Unbalanced Mixed Linear Models

摘要

This document presents a general procedure for obtaining exact confidence regions for the variance components in unbalanced mixed linear models. The procedure utilizes, as pivotal quantities, quadratic forms that may depend on the variance components in a complicated way and that are distributed independently as chi-square variates. In the special case of balanced classificatory models, the pivotal quantities simplify to scalar multiples of sums of squares from the usual analysis of variance. The procedure can be easily modified so as to obtain an exact confidence region for ratios of variance components and can be regarded as a generalization of Wald's procedure for obtaining a confidence interval for a single variance ratio. (Author)