The equality between linear transforms of ordinary least squares and best linear unbiased estimator

Jürgen Groß; Götz Trenkler

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.

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Year of publication:	1998
Authors:	Groß, Jürgen ; Trenkler, Götz
Publisher:	Dortmund : SFB 475, Universität Dortmund
Subject:	Ordinary least squares estimator \| best linear unbiased estimator \| prediction \| linear transform \| orthogonal projector \| Schätztheorie \| Estimation theory \| Kleinste-Quadrate-Methode \| Least squares method