Discussiones Mathematicae Probability and Statistics 25(1) (2005) 39-49

EXTENSIONS OF THE
FRISCH-WAUGH-LOVELL THEOREM

Jürgen Groß

Department of Statistics, University of Dortmund
Vogelpothsweg 87, D-44221 Dortmund, Germany

e-mail gross@amadeus.statistik.uni-dortmund.de

Simo Puntanen

Department of Mathematics, Statistics and Philosophy
FI-33014 University of Tampere, Finland

e-mail sjp@uta.fi

Abstract

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.

2000 Mathematics Subject Classification: 62J05, 62H12.

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Received 15 December 2003