Inverse-partitioned-matrix method for the general Gauss-Markov model with linear restrictions

Abstract

Abstract The inverse-partitioned-matrix method, introduced by Rao (1971) for statistical inference in the general Gauss-Markov model M={y, Xβ , σ 2 V } , is adopted to represent (i) the consistency condition, (ii) the minimum dispersion linear unbiased estimators of estimable linear functions of β , and (iii) the minimum norm quadratic unbiased estimator of σ 2 , all corresponding to the model M merged with linear restrictions Rβ = r , in terms referring explicitly to the unrestricted model M and the restrictions. These representations are then applied to derive necessary and sufficient conditions under which information contained in the restrictions is negligible.