Linear Estimation with an Incorrect Dispersion Matrix in Linear Models with a Common Linear Part

Abstract

The linear model ( Y, X β, V ), where X is any matrix satisfying the conditions ℛ ( U ) ⊂ ℛ ( X ) and ℛ ( A ′) ⊂ ℛ ( X′ ), is considered, U and A being known matrices and ℛ (·) denoting range space. Nonnegative definite matrices V , for which every linear representation or some linear representation of the BLUE of A β under ( Y, X β, V 1 ) continues to be its BLUE under ( Y, X β, V ) for every such matrix X , are characterized. Conditions under which estimable linear parametric functions admit a BLUE for the variance components model are also given.