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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 multiplecorrelation coefficient in a linear model according to the coefficientsof correlation. This expression makes it possible to analyze from anumerical point of view the instability of estimates in the case ofcollinear explanatory variables in the linear model or in theautoregressive model. This numerical approach, that we show on twoexamples, thus supplements the usual approach of the quasi colinearity,founded on the statistical properties of the estimators.

Keywords

Linear multiple modelcollinearitymultiple correlationcoefficientssymmetric definite positive matrixCholesky'sfactorization.Modèle linéaire multiplequasi colinéaritécoefficients decorrélation multiplematrice symétrique définie positivefactorisationde 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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