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Tutz, Gerhard; Petry, Sebastian (21. Mai 2013): Generalized Additive Models with Unknown Link Function Including Variable Selection. Department of Statistics: Technical Reports, Nr. 145
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Abstract

The generalized additive model is a well established and strong tool that allows to model smooth effects of predictors on the response. However, if the link function, which is typically chosen as the canonical link, is misspecified, substantial bias is to be expected. A procedure is proposed that simultaneously estimates the form of the link function and the unknown form of the predictor functions including selection of predictors. The procedure is based on boosting methodology, which obtains estimates by using a sequence of weak learners. It strongly dominates fitting procedures that are unable to modify a given link function if the true link function deviates from the fixed function. The performance of the procedure is shown in simulation studies and illustrated by a real world example.