Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models
Article first published online: 13 JUN 2011
© 2011, The International Biometric Society
Volume 68, Issue 1, pages 31–44, March 2012
How to Cite
Croux, C., Gijbels, I. and Prosdocimi, I. (2012), Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models. Biometrics, 68: 31–44. doi: 10.1111/j.1541-0420.2011.01630.x
- Issue published online: 23 MAR 2012
- Article first published online: 13 JUN 2011
- Received September 2010. Revised April 2011. Accepted April 2011.
- Generalized additive modeling;
- Mean regression function;
- Robust estimation
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.