An elementary development of the equation characterizing best linear unbiased estimators

✍ Scribed by Jerzy K Baksalary

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 157 KB
• Volume: 388
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00396-3

✦ Synopsis

Puntanen 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 X under the general Gauss-Markov model M = {y, X , σ 2 V} 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 K . From the algebraic point of view, the present development seems to be the simplest from among all accessible in the literature till now.