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

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 is straightforward in contrast to the classic form. An example: 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.