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Knüsel, Leo (2009): The General Linear Model and the Generalized Singular Value Decomposition; Some Examples. Department of Statistics: Technical Reports, No.49
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Abstract

The general linear model with correlated error variables can be transformed by means of the generalized singular value decomposition to a very simple model (canonical form) where the least squares solution is obvious. The method works also if X and the covariance matrix of the error variables do not have full rank or are nearly rank deficient (rank-k approximation). By backtransformation one obtains the solution for the original model. In this paper we demonstrate the method with some examples.