Testing linear forms of variance components by generalized fixed-level tests

Abstract

This report extends the technique of testing single variance components with generalized fixed-level tests - in situations when nuisance parameters make exact testing impossible - to the more general way of testing hypotheses on linear forms of variance components. An extension of the definition of a generalized test variable leads to a generalized fixed-level test for arbitrary linear hypotheses on variance components in balanced mixed linear models of the ANOVA-type. For point null hypotheses an alternative for the known method is given, which ist straightforward in contrast to the classic form. An example (2-way nested classification with random effects) illustrates the way how to use the results and simulation studies are carried out to prove the quality of the presented methods.