Linear models with variance-covariance components are used in awide 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 modelswhere 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 linearhypotheses 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 severaldecades. 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 afew 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.
@article{172,
title = {On exact inference in linear models with two variance-covariance components},
journal = {Tatra Mountains Mathematical Publications},
volume = {51},
year = {2012},
doi = {10.2478/tatra.v51i1.172},
language = {EN},
url = {http://dml.mathdoc.fr/item/172}
}
Volaufová, Júlia; Witkovský, Viktor. On exact inference in linear models with two variance-covariance components. Tatra Mountains Mathematical Publications, Tome 51 (2012) . doi : 10.2478/tatra.v51i1.172. http://gdmltest.u-ga.fr/item/172/