One- and Two-Sided Tolerance Intervals for General Balanced Mixed Models and Unbalanced One-Way Random Models

Abstract

In this article we develop procedures for one- and two-sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi-squared random variables. The proposed procedures are based on the concept of generalized pivotal quantities and are applicable to general mixed models provided that balanced data are available. However, this study focuses on situations involving unbalanced data. Specific attention is given to the unbalanced one-way random model. It is shown that the use of generalized pivotal quantities allows the construction of the tolerance intervals of interest fairly straightforward. Some practical examples are given to illustrate the proposed procedures. Furthermore, detailed statistical simulation studies are conducted to evaluate their performance, showing that the proposed procedures can be recommended for practical use.

KEY WORDS :

• Chi-squared approximation
• Generalized confidence interval
• Generalized p value
• Linear model
• Variance component