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Colinearité et Instabilité Numérique dans le Modèle Linéaire

Published online by Cambridge University Press:  15 August 2002

Thierry Foucart
Thierry Foucart*
Affiliation:
Département Mathématiques, S P 2 M I, boulevard 3, Téléport 2, BP. 179, 86960 Futuroscope Cedex, France.
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Abstract

In this paper we give the expression of the multiple correlation coefficient in a linear model according to the coefficients of correlation. This expression makes it possible to analyze from a numerical point of view the instability of estimates in the case of collinear explanatory variables in the linear model or in the autoregressive model. This numerical approach, that we show on two examples, thus supplements the usual approach of the quasi colinearity, founded on the statistical properties of the estimators.

Keywords

Linear multiple modelcollinearitymultiple correlation coefficientssymmetric definite positive matrixCholesky's factorization.Modèle linéaire multiplequasi colinéaritécoefficients de corrélation multiplematrice symétrique définie positivefactorisation de Cholesky.
Type
Research Article
Information
RAIRO - Operations Research , Volume 34 , Issue 2 , April 2000 , pp. 199 - 212
Copyright
© EDP Sciences, 2000

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