Optimum Tests for Fixed Effects and Variance Components in Balanced Models

摘要

For any ANOVA model with balanced data involving both fixed and random effects, UMPU and UMPI tests are derived for the significance of a fixed effect or a variance component, under the assumption of normality of random effects. The tests coincide with the usual F-tests. Robustness of the UMPI test against suitable deviations from normality is established. Keywords: Balanced models, Fixed effects, Random effects, Variance components, UMPI, UMPU, Elliptically symmetric distributions.