TESTING HYPOTHESES IN MIXED LINEAR-MODELS

The paper proposes a new class of tests for variance components in general mixed models. A selective literature survey on testing hypotheses in unbalanced mixed analysis of variance shows the need of a theory of approximate tests. Using a compromise on unbiasedness a new optimality criterion is introduced. It is shown that C.R. Rao's MINQUE is locally sufficient in this context, and the class of locally best locally unbiased invariant tests is constructed. Examples show a good approximation of the nominal significance level on a large region of the hypothesis and a high power of the resulting test.