accident risk — 1 articles found.

A confidence interval estimation problem using the Schur complement approach with application

C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (3), 2005 pp. 84–91
Vol.27 (3) 2005
Assi N'Guessan; Francois Bellavance Details
(Received: 2005-03-14 )
(Received: 2005-03-14 )

Assi N'Guessan, Polytech’Lille and Laboratoire,Paul Painleve CNRS, UMR 8542, Universite de Lille 1, Bat. Polytech’Lille, 59655 Villeneuve d’Ascq Cedex, France; email: assi.nguessan@polytech-lille.fr

Francois Bellavance, HEC Montr ́eal and Laboratory, Transportation Safety Centre for Research on Transportation, Universite de Montreal, P.O. Box 6128, Succ. Centre-ville, Montreal, H3C 3J7francois.bellavance@hec.ca

Abstract/Résumé:

We present a method based on the Schur complement approach to build asymptotic confidence intervals linked to the maximum likelihood estimator of a vector of parameters under constraints. This approach makes it possible to obtain the formal expression of the standard error of each component of the vector without direct inversion of the Fisher information matrix. We then give an application of this method to the modelling and the confidence interval estimation of the average effect of a road safety measure and the accident risks of different types.

Nous proposons une méthode basée sur la technique du complément de Schur pour construire des intervalles de confiance asymptotiques relatifs à l’estimateur du maximum de vraisemblance d’un vecteur paramètre soumis à des contraintes. Cette méthode permet d’obtenir l’expression formelle de l’écart-type de chaque composante du vecteur sans inverser directement la matrice d’information de Fisher. Nous indiquons ensuite une application de cette méthodologie à la modélisation et à l’estimation par intervalle de confiance de l’effet moyen d’une mesure de sécurité routière et de différents risques d’accident.

Keywords: Fisher information matrix, Schur complement, accident data., accident risk, confidence interval, constrained maximum likelihood, formal asymptotic variance, logistic multinomial model, road safety measure

AMS Subject Classification: Matrix inversion; generalized inverses 15A09

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