Geodesic
Generalized F tests and selective generalized F tests for orthogonal and associated mixed models
Discussiones Mathematicae. Probability and Statistics, Tome 28 (2008) no. 2, pp. 229-246

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The statistics of generalized F tests are quotients of linear combinations of independent chi-squares. Given a parameter, θ, for which we have a quadratic unbiased estimator, θ̃, the test statistic, for the hypothesis of nullity of that parameter, is the quotient of the positive part by the negative part of such estimator. Using generalized polar coordinates it is possible to obtain selective generalized F tests which are especially powerful for selected families of alternatives. We build both classes of tests for the orthogonal and associated mixed models. The associated models are obtained adding terms to the orthogonal models.
Keywords: selective generalized F tests, generalized polar coordinates, associated models 
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     title = {Generalized {F} tests and selective generalized {F} tests for orthogonal and associated mixed models},
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Nunes, Célia; Pinto, Iola; Mexia, João. Generalized F tests and selective generalized F tests for orthogonal and associated mixed models. Discussiones Mathematicae. Probability and Statistics, Tome 28 (2008) no. 2, pp. 229-246. http://geodesic.mathdoc.fr/item/DMPS_2008_28_2_a3/