Geodesic
Estimators and tests for variance components in cross nested orthogonal designs
Discussiones Mathematicae. Probability and Statistics, Tome 23 (2003) no. 2, pp. 175-201.

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Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.
Keywords: hypothesis testing, generalized F distribution, adaptative test, nested orthogonal designs 
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Fonseca, Miguel; Mexia, João; Zmyślony, Roman. Estimators and tests for variance components in cross nested orthogonal designs. Discussiones Mathematicae. Probability and Statistics, Tome 23 (2003) no. 2, pp. 175-201. http://geodesic.mathdoc.fr/item/DMPS_2003_23_2_a5/

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