The General Linear Model and the Generalized Singular Value Decomposition; Some Examples

Knüsel, Leo (2009): The General Linear Model and the Generalized Singular Value Decomposition; Some Examples. Department of Statistics: Technical Reports, Nr. 49

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.

• Dokumententyp: Paper
• Keywords: General linear model, canonical form, generalized singular value decomposition, CS-decomposition of an orthogonal matrix, multicollinearity, rank-k approximation.
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Technische Reports
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch