Confidence Intervals and Sets for Linear Combinations of Fixed and Random Effects

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Abstract
Confidence regions are constructed for linear combinations of fixed effects and realized or sample values of random effects. These regions can be used in instances where the ratios of the variance components can be regarded as known. They have the prescribed long-run, frequency of coverage when there is repeated sampling of the random effects as well as the residual effects. They have smaller expected volume than confidence regions obtained by proceeding as though the random effects are fixed effects. Mixed and random linear models, such as those that underlie the analysis of variance (ANOVA) are often applied to biological and agricultural data.

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