Generalized Additive Models with Unknown Link Function Including Variable Selection

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.