, Volume 19, Issue 3, pp 580–608

Nonparametric estimation of mean and dispersion functions in extended generalized linear models

Original Paper

DOI: 10.1007/s11749-010-0187-1

Cite this article as:
Gijbels, I., Prosdocimi, I. & Claeskens, G. TEST (2010) 19: 580. doi:10.1007/s11749-010-0187-1


We study joint nonparametric estimators of the mean and the dispersion functions in extended double exponential family models. The starting point is the exponential family and the generalized linear models setting. The extended models allow for both overdispersion and underdispersion, or even a combination of both. We simultaneously estimate the dispersion function and the mean function by using P-splines with a difference type of penalty to avoid overfitting. Special attention is given to the smoothing parameter selection as well as to implementation issues. The performance of the method is investigated via simulations. A comparison with other available methods is made. We provide applications to several sets of data, including continuous data, counts and proportions.


Double exponential familyExtended quasi-likelihoodNonparametric regressionOverdispersionP-splinesVariance estimationUnderdispersion

Mathematics Subject Classification (2000)


Copyright information

© Sociedad de Estadística e Investigación Operativa 2010

Authors and Affiliations

  1. 1.Department of MathematicsKatholieke Universiteit LeuvenLeuvenBelgium
  2. 2.Leuven Statistics Research Center (LStat)Katholieke Universiteit LeuvenLeuvenBelgium
  3. 3.Operations Research and Business StatisticsKatholieke Universiteit LeuvenLeuvenBelgium