Stat Papers (2009) 50:721–733 DOI 10.1007/s00362-009-0252-6 A projector oriented approach to the best linear unbiased estimator Oskar Maria Baksalary · Götz Trenkler Received: 30 September 2008 / Accepted: 13 April 2009 / Published online: 7 August 2009 © Springer-Verlag 2009 Abstract The paper provides a projector based approach to the best linear unbiased estimator (BLUE). By revisiting the so called generalized projection operator, intro- duced in Rao (J R Stat Soc Ser B Stat Methodol 36:442–448, 1974), a number of new formulae for BLUE is established. Furthermore, some attention is paid to the coincidence of the BLUE and the ordinary least squares estimator. Keywords General Gauss–Markov model · Ordinary least squares estimator · Oblique projector · Generalized projection operator Mathematics Subject Classification (2000) 62J05 · 62H12 · 15A24 · 15A57 1 Introduction Let us consider the general Gauss–Markov model y = Xβ + u, (1.1) where y is an n × 1 observable random vector, X is a known n × p model matrix, β is a p × 1 vector of unknown parameters, and u is an n × 1 random error vector. O. M. Baksalary Faculty of Physics, Adam Mickiewicz University, ul.Umultowska 85, 61-614 Poznan, Poland O. M. Baksalary (B ) · G. Trenkler Department of Statistics, Dortmund University of Technology, Vogelpothsweg 87, 44221 Dortmund, Germany e-mail: baxx@amu.edu.pl G. Trenkler e-mail: trenkler@statistik.uni-dortmund.de 123