Uniformly minimum variance unbiased estimation in various classes of estimators, I.2

Two main classes of estimators for parametric functions in linear models are considered, the class Γ 1 of quadratic estimators and the class Γ 2 of linear plus quadratic estimators. Let G i, i=1,2, be the class of functions for which there exist an unbiased estimator in Γ i Necessary and sufficient conditions for a given estimator in Γ i, i =1,2 to be a minimum variance estimator for its expected value are presented. Moreover, necessary and sufficient conditions for each g∈i, i =1,2,1, 2, to have an uniformly minimum variance estimator in Γ i are given. Similar problems are also discussed for 3 defined subclasses of Γ 1 and for 4 subclasses of Γ 2. Finally necessary and sufficient conditions are given for the simultaneous existence of a best linear estimator and a best quadratic estimator.