Confidence Regions for Variance Ratios of Random Models

Abstract

There appears to be no standard method of constructing confidence regions for the variance components and ratios of a random or mixed model; however, with regard to point estimation and tests of hypotheses the analysis of variance has become somewhat routine. This study derives confidence regions by using the AOV mean squares with Kimball's result. These confidence regions are conservative, that is, the actual confidence level cannot be less than any pre-set value and are polygonal and easy to construct. They determine simultaneous confidence intervals for the variance ratios, but these intervals (one-sided) have the defect that the end-point may be negative, a property similar to that of the AOV estimators of variance components. Confidence regions are demonstrated for the two-way classification and three-stage nested model and a numerical example is included.