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Knüsel, Leo (2008): Singulärwert-Zerlegung und Methode der kleinsten Quadrate. Department of Statistics: Technical Reports, No.31
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Abstract

The method of least squares is an important instrument to determine the optimal linear estimators in regression models. By means of the singular value decomposition we can find the least squares estimators without differentiation, without solving the normal equations and without assumptions on the rank of the data matrix. Even in case of multicollinearity we can find the simple and natural solutions. The results in the paper are not new, they have been developed mainly in numerical publications, but they are hardly to be found in statistical textbooks.