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

C. Croux, I. Gijbels, I. Prosdocimi

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Abstract

Generalized Linear Models are a widely used method to obtain parametric es- timates for the mean function. They have been further extended to allow the re- lationship 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 covari- ates. 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 dispersion 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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages21
Volume2010-104
Publication statusPublished - 2010

Publication series

NameCentER Discussion Paper
Volume2010-104

Keywords

  • dispersion
  • generalized additive modelling
  • mean regression function
  • quasilikelihood
  • M-estimation
  • P-splines
  • robust estimation

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