Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models

CentER Discussion Paper Series No. 2010-104

21 Pages Posted: 13 Oct 2010

See all articles by Christophe Croux

Christophe Croux

KU Leuven - Faculty of Business and Economics (FEB)

Irene Gijbels

Catholic University of Louvain (UCL) - School of Statistics

Ilaria Prosdocimi

KU Leuven - Department of Mathematics

Multiple version iconThere are 3 versions of this paper

Date Written: September 3, 2010

Abstract

Generalized Linear Models are a widely used method to obtain parametric estimates for the mean function. They have been further extended to allow the relationship between the mean function and the covariates to be more flexible via Generalized Additive Models. However the fixed variance structure can in many cases be too restrictive. The Extended Quasi-Likelihood (EQL) framework allows for estimation of both the mean and the dispersion/variance as functions of covariates. As for other maximum likelihood methods though, EQL estimates are not resistant to outliers: we need methods to obtain robust estimates for both the mean and the dspersion function. In this paper we obtain functional estimates for the mean and the dispersion that are both robust and smooth. The performance of the proposed method is illustrated via a simulation study and some real data examples.

Keywords: dispersion, generalized additive modelling, mean regression function, quasilikelihood, M-estimation, P-splines, robust estimation

JEL Classification: C13, C14

Suggested Citation

Croux, Christophe and Gijbels, Irene and Prosdocimi, Ilaria, Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models (September 3, 2010). CentER Discussion Paper Series No. 2010-104, Available at SSRN: https://ssrn.com/abstract=1690487 or http://dx.doi.org/10.2139/ssrn.1690487

Christophe Croux (Contact Author)

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Irene Gijbels

Catholic University of Louvain (UCL) - School of Statistics ( email )

Voie du Roman Pay
34 B-1348 Louvain-La-Neuve, 1348
Belgique
+32 10-474306 (Phone)

Ilaria Prosdocimi

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

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