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

Authors

  • Christophe Croux,

    1. Faculty of Business and Economics, Katholieke Universiteit Leuven, Naamsestraat 69, Box 3555, B-3000 Leuven, Belgium
    2. Leuven Statistics Research Center (LStat), Katholieke Universiteit Leuven, Celestijnenlaan 200B, Box 5307, B-3001 Leuven (Heverlee), Belgium
    3. Tilburg University, CentER, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
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  • Irène Gijbels,

    Corresponding author
    1. Leuven Statistics Research Center (LStat), Katholieke Universiteit Leuven, Celestijnenlaan 200B, Box 5307, B-3001 Leuven (Heverlee), Belgium
    2. Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, Box 2400, B-3001 Leuven (Heverlee), Belgium
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  • Ilaria Prosdocimi

    1. Leuven Statistics Research Center (LStat), Katholieke Universiteit Leuven, Celestijnenlaan 200B, Box 5307, B-3001 Leuven (Heverlee), Belgium
    2. Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, Box 2400, B-3001 Leuven (Heverlee), Belgium
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email: Irene.Gijbels@wis.kuleuven.be

Abstract

Summary 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.

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