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

Abstract

The linear model (Y, Xβ, 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 Aβ under (Y, Xβ, V ₁) continues to be its BLUE under (Y, Xβ, 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.

Key Words:

• Ordinary least squares estimator
• Best linear unbiased estimator
• Variance components model