: In this paper we derive asymptotic 2 --tests for general linear hypotheses on variance components using repeated variance components models. In two examples, the two--way nested classification model and the two--way crossed classification model with interaction, we explicitly investigate the properties of the asymptotic tests in small sample sizes. Key Words: Wald-- and likelihood ratio test statistic, repeated variance components model, linear hypotheses on variance components 1 Introduction In this paper we consider linear hypotheses on variance components as H 0 : Koe = d ; (1) where oe = (oe 2 1 ; : : : ; oe 2 m ) T denotes a vector of unknown variance components, K is a known (p \Theta m)--matrix with rk (K) = p m and d 2 IR p a known constant. For special linear combinations of variance components exact F -- and 2 --tests can be derived and in El-- Bassiouni and Seely (1980) it is shown that under certain circumstances these tests are uniformly most powerful unbia..
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