Flexible Mean and Dispersion Function Estimation in Extended Generalized Additive Models

Real data may expose a larger (or smaller) variability than assumed in an exponential family modeling, the basis of Generalized linear models and additive models. To analyze such data, smooth estimation of the mean and the dispersion function has been introduced in extended generalized additive mode...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 41; no. 16-17; pp. 3259 - 3277
Main Authors Gijbels, I., Prosdocimi, I.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 01.08.2012
Taylor & Francis Ltd
Subjects
Additive modeling
Dispersion function
Double exponential family
Economic models
Generalized linear models
Mean function
Nonparametric estimation
P-splines approximation
Studies
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Summary:Real data may expose a larger (or smaller) variability than assumed in an exponential family modeling, the basis of Generalized linear models and additive models. To analyze such data, smooth estimation of the mean and the dispersion function has been introduced in extended generalized additive models using P-splines techniques. This methodology is further explored here by allowing for the modeling of some of the covariates parametrically and some nonparametrically. The main contribution in this article is a simulation study investigating the finite-sample performance of the P-spline estimation technique in these extended models, including comparisons with a standard generalized additive modeling approach, as well as with a hierarchical modeling approach.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2012.654881