An elementary development of the equation characterizing best linear unbiased estimators

AbstractPuntanen et al. [J. Statist. Plann. Inference 88 (2000) 173] provided two matrix-based proofs of the result stating that a linear estimator By represents the best linear unbiased estimator (BLUE) of the expectation vector Xβ under the general Gauss–Markov model M={y,Xβ,σ2V} if and only if B(X:VX⊥)=(X:0), where X⊥ is any matrix whose columns span the orthogonal complement to the column space of X. In this note, still another development of such a characterization is proposed with reference to the BLUE of any vector of estimable parametric functions Kβ. From the algebraic point of view, the present development seems to be the simplest from among all accessible in the literature till now