Geodesic
Selective generalized F tests
Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 2, pp. 281-288.

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Generalized F tests were introduced by Michalski and Zmyślony (1996) for variance components and later (1999) for linear functions of parameters in mixed linear models. We now use generalized polar coordinates to obtain, for the second case, tests that are more powerful for selected families of alternatives.
Keywords: mixed linear models, variance components, generalized polar coordinates, selective F testes 
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Nunes, C.; Mexia, J. Selective generalized F tests. Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 2, pp. 281-288. http://geodesic.mathdoc.fr/item/DMPS_2004_24_2_a6/

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[2] A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mountain Mathematical Publications 17 (1999), 103-110.

[3] C. Nunes and J.T. Mexia, Selective F tests for sub-normal models, Discussiones Mathematicae, Probability and Statistics 23 (2003), 167-174.

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[6] M.G. Kendall, A Ccourse in the Geometry of n Dimensions, Charles Griffin Company Limited, London 1961.