Abstract
Abstract Interval estimation of certain functions of variance components is of interest to research workers in all fields of applications in which the variance component model is used. Confidence intervals for linear functions and ratios of variance components have been proposed by several authors. For the most part, these intervals are approximate with unknown exact probabilities associated with their coverage. In this article a technique is given for the construction of simultaneous confidence intervals for the values of all continuous functions of the variance components in a balanced, general random linear model. These confidence intervals are conservative; that is, the actual confidence level cannot be less than any preset value. The proposed technique is easy to apply as it only requires the optimization of a given continuous function of the variance components over a bounded region. Several examples of continuous functions are considered, including linear functions and ratios of variance components. Furthermore, the technique can be applied to unbalanced, random two-way classification models.
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