Generalized additive models with unknown link function including variable selection. Issue 15 (17th November 2016)

• Record Type: Journal Article
• Authors: Tutz, Gerhard; Petry, Sebastian
• Is Part Of: Journal of applied statistics. Volume 43:Issue 15(2016)
• Page Start: 2866
• Page End: 2885
• Publication Date: 2016-11-17
• Subjects: Variable selection -- generalized additive models -- single index models -- link function estimation; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2016.1155109
• Languages: English
• ISSNs: 0266-4763

Abstract

ABSTRACT: The generalized additive model is a well established and strong tool that allows modelling smooth effects of predictors on the response. However, if the link function, which is typically chosen as the canonical link, is misspecified, estimates can be biased. 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 real world examples.