Geodesic
Extensions of the Frisch-Waugh-Lovell Theorem
Discussiones Mathematicae. Probability and Statistics, Tome 25 (2005) no. 1, pp. 39-49

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In this paper we introduce extensions of the so-called Frisch-Waugh-Lovell Theorem. This is done by employing the close relationship between the concept of linear sufficiency and the appropriate reduction of linear models. Some specific reduced models which demonstrate alternatives to the Frisch-Waugh-Lovell procedure are discussed.
Keywords: best linear unbiased estimation, Frisch-Waugh-Lovell Theorem, linear sufficiency, orthogonal projector, partitioned linear model, reduced linear model 
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Groß, Jürgen; Puntanen, Simo. Extensions of the Frisch-Waugh-Lovell Theorem. Discussiones Mathematicae. Probability and Statistics, Tome 25 (2005) no. 1, pp. 39-49. http://geodesic.mathdoc.fr/item/DMPS_2005_25_1_a1/