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

Rok, strany: 2012, 173 - 181

Linear models with variance-covariance components are used in a wide variety of applications. In most situations it is possible to partition the response 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 alternative 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 multivariate normal distribution, it is not clear what test to recommend except in a few settings such as balanced or orthogonal designs. Here we investigate statistical properties, such as accuracy of $p$-values and powers of exact (Crainiceanu & Ruppert 2004) tests and compare with properties of approximate asymptotic tests. Simultaneous exact confidence regions for variance components and mean parameters are constructed as well.

ISO 690:

Volaufová, J., Witkovský, V. 2012. On exact inference in linear models with two variance-covariance components. In Tatra Mountains Mathematical Publications, vol. 51, no.1, pp. 173-181. 1210-3195.

APA:

Volaufová, J., Witkovský, V. (2012). On exact inference in linear models with two variance-covariance components. Tatra Mountains Mathematical Publications, 51(1), 173-181. 1210-3195.