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, No.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.

• Item Type: Paper (Technical Report)
• Keywords: General linear model, canonical form, generalized singular value decomposition, CS-decomposition of an orthogonal matrix, multicollinearity, rank-k approximation.
• Collections: Mathematics, Computer Science and Statistics > Statistics > Technical Reports
• Subjects: 500 Science > 510 Mathematics
• Language: English