A Simple General Method for Constructing Confidence Intervals for Functions of Variance Components

Abstract

A simple general method is proposed for constructing confidence intervals for arbitrary functions of variance components in balanced normal-theory models. The concept of “surrogate variables” is introduced as part of the description of the method. “Equal-tail” and “shortest-length” confidence intervals from this method can be computed easily using simulations. As an illustration, the two-way random-effects model is considered. It is shown that the proposed method produces intervals that are comparable in confidence coefficient and average length to those produced by the best existing methods.

KEY WORDS :

• ANOVA
• Balanced models
• Gauge R&R
• Modified large-sample method
• Surrogate variables
• Two-way random-effects model