Abstract
The main purpose of this paper is the use of best linear unbiased estimates in order to build F tests with duality properties. The relationship between those properties and the Scheffé multiple comparison method is analyzed. A situation of controlled heteroscedasticity, in which the vector of observations has a variance-covariance matrix σ 2 C, with C known and regular, is considered and full-rank is not assumed. The paper comprises, besides an introduction, four sections. In the first of these, Moore—Pemrose inverses are used to obtain orthogonal projection matrices. These orthogonal projection matrices are then used, in the following section, to obtain best linear unbiased estimates of estimable vectors. In obtaining these estimates the reduction of the controlled heteroscedasticity of the vector of observations is carried through. Once obtained the best linear unbiased estimates the construction of the F tests is performed. The F tests that are obtained are unbiased and possess duality. In a final section the relation between the duality of the F tests and the Scheffé multiple comparisons method is considered.
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