Admissible linear estimation in the general Gauss-Markov model with respect to an arbitrary quadratic risk function

Abstract

In the first part of this paper, we give a complete characterization of the class, A_W(Kβ) of all estimators that are admissible for any given vector of parametric functions Kβ, not necessarily identifiable, among the set of linear estimators under the general Gauss-Markov model M = {Y, Xβ, σ²V}, with both the model matrix X and the dispersion matrix V possibly deficient in rank, when the criterion for comparing estimators is the W-weighted quadratic risk function, with any nonnegative definite weight-matrix W. In the second part, we investigate the robustness of the class A_W(Kβ) with respect to W, with the conclusion that, except for special situations only, there is full freedom in choosing W within the set of matrices having the same range.