The equality between linear transforms of ordinary least squares and best linear unbiased estimator - Jürgen Groß; Götz Trenkler (Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 1998)
The best linear unbiased estimator BLUE (CXb) of a linear transform CX b in the general Gauss-Markov model (y, E (y) = X b Cov (y) =a2v) is the linear transform C BLUE (Xb) of the best linear unbiased estimator BLUE (Xb) of Xb. Similarly, for the ordinary least squares estimator OLSE (CXb) = C OLSE (X) . The problem of equality of OLSE (Xb) and BLUE (Xb) has been widely discussed in the literature. In this note, characterizations of the equality COLSE (Xb) = CBLUE (Xb) are given in terms of projectors and subspaces.
Keywords: 519; Ordinary least squares estimator; best linear unbiased estimator; prediction; linear transform; orthogonal projector