Robust estimation of mean and dispersion functions in extended generalized additive models

Christophe Croux, Irène Gijbels, Ilaria Prosdocimi

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

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 quasilikelihood (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 dispersion function. In this article, 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
Pages (from-to)31-44
Number of pages14
JournalBiometrics
Volume68
Issue number1
DOIs
Publication statusPublished - Mar 2012

Keywords

  • Dispersion
  • Generalized additive modeling
  • M-estimation
  • Mean regression function
  • P-splines
  • Quasilikelihood
  • Robust estimation

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