Geodesic
F-tests for generalized linear hypotheses in subnormal models
Discussiones Mathematicae. Probability and Statistics, Tome 21 (2001) no. 1, pp. 49-62

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When the measurement errors may be assumed to be normal and independent from what is measured a subnormal model may be used. We define a linear and generalized linear hypotheses for these models, and derive F-tests for them. These tests are shown to be UMP for linear hypotheses as well as strictly unbiased and strongly consistent for these hypotheses. It is also shown that the F-tests are invariant for regular transformations, possess structural stability and are almost strongly consistent for generalized linear hypothesis. An application to a mixed model studied by Michalskyi and Zmyślony is shown.
Keywords: F-tests, subnormal models, mixed models, invariance, UMP tests, third type error 
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Mexia, Joao; Dias, Gerberto. F-tests for generalized linear hypotheses in subnormal models. Discussiones Mathematicae. Probability and Statistics, Tome 21 (2001) no. 1, pp. 49-62. http://geodesic.mathdoc.fr/item/DMPS_2001_21_1_a3/