Exact distributions of statistics for making inferences on mixed models under the default covariance structure

At this juncture when mixed models are heavily employed in applications ranging from clinical research to business analytics, the purpose of this article is to extend the exact distributional result of Wald (Ann. Math. Stat. 18: 586–589, 1947) to handle models involving a number of variance components.Due to the unavailability of exact distributional results for underlying statistics, currently available methods provide small group/sample inference only for balanced ANOVA models or simple regression models. The exact distributional results developed in this article should prove useful in making inferences by such methods as parametric bootstrap, fiducial, and generalized p-value approach, when there are a number of variance components to deal with.