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On ordinary ridge regression in generalized linear models
Umeå University, Faculty of Social Sciences, Department of Statistics.
1992 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, ISSN 0361-0926, Vol. 21, no 8, 2227-2246 p.Article in journal (Refereed) Published
Abstract [en]

In this paper it is shown that an ill-conditioned data matrix has similar effects on the parameter estimator when estimating generalized linear models as when estimating linear regression models. Asymptotically, the average length of the maximum likelihood estimator of a parameter vector increases as the conditioning of the covariance matrix deteriorates. A generalization of the ridge regression is suggested for maximum likelihood estimation in generalized linear models. In particular the existence of a ridge coefficient, k, such that the asymptotic mean square error of the generalized linear model ridge estimator is smaller than the asymptotic variance of the maximum likelihood estimator is shown. A numerical example illustrates the theoretical results

Place, publisher, year, edition, pages
Philadelphia: Taylor & Francis , 1992. Vol. 21, no 8, 2227-2246 p.
Keyword [en]
Bootstrap, Maximum likelihood, Maximum vraisemblance, Generalized linear model, Modèle linéaire généralisé, Ridge regression, Régression ridge, Mean square error, Erreur quadratique moyenne, Optimization, Optimisation, Matrice mal conditionnée
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-46791OAI: oai:DiVA.org:umu-46791DiVA: diva2:441300
Available from: 2011-09-15 Created: 2011-09-14 Last updated: 2017-12-08Bibliographically approved

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