On geometry of the set of admissible invariant quadratic estimators in balanced two variance components model

Abstract

Two variance components model for which each invariant quadratic admissible estimator of a linear function of variance components (under quadratic loss function) is a linear combination of two quadratic forms,Z1,Z2, say, is considered. A setD={(d1,d2)′:d1Z1+d2Z2 is admissible} is described by giving formulae on the boundary ofD. Different forms of the setD are presented on figures.