Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models
CentER Discussion Paper Series No. 2010-104
21 Pages Posted: 13 Oct 2010
There are 3 versions of this paper
Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models
Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models
Date Written: September 3, 2010
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 Quasi-Likelihood (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 dspersion 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.
Keywords: dispersion, generalized additive modelling, mean regression function, quasilikelihood, M-estimation, P-splines, robust estimation
JEL Classification: C13, C14
Suggested Citation: Suggested Citation