On exact inference in linear models with two variance-covariance components

Abstract

Linear models with variance-covariance components are used in a wide variety of applications. In most situations it is possible to partition the re-sponse vector into a set of independent subvectors, such as in longitudinal models where the response is observed repeatedly on a set of sampling units (see, e.g., Laird & Ware 1982). Often the objective of inference is either a test of linear hypotheses about the mean or both, the mean and the variance components. Confidence intervals for parameters of interest can be constructed as an alter-native to a test. These questions have kept many statisticians busy for several decades. Even under the assumption that the response can be modeled by a mul-tivariate normal distribution, it is not clear what test to recommend except in a few settings such as balanced or orthogonal designs. Here we investigate statis-tical properties, such as accuracy of p-values and powers of exact (Crainiceanu & Ruppert 2004) tests and compare with properties of approximate asymptotictests. Simultaneous exact confidence regions for variance components and meanparameters are constructed as well. © 2012 Mathematical Institute, Slovak Academy of Sciences.