Generalized F tests and selective generalized F tests for orthogonal and associated mixed models

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, θe, the test statistic, for thehypothesis of nullity of that parameter, is the quotient of the positivepart by the negative part of such estimator. Using generalized polarcoordinates it is possible to obtain selective generalized F tests whichare especially powerful for selected families of alternatives.We build both classes of tests for the orthogonal and associatedmixed models. The associated models are obtained adding terms tothe orthogonal models.