  Smooth backfitting was first introduced in an additive regression setting via
a direct projection alternative to the classic backfitting method by Buja,
Hastie and Tibshirani. This paper translates the original smooth backfitting
concept to a survival model considering an additively structured hazard. The
model allows for censoring and truncation patterns occurring in many
applications such as medical studies or actuarial reserving. Our estimators are
shown to be a projection of the data into the space of multivariate hazard
functions with smooth additive components. Hence, our hazard estimator is the
closest nonparametric additive fit even if the actual hazard rate is not
additive. This is different to other additive structure estimators where it is
not clear what is being estimated if the model is not true. We provide full
asymptotic theory for our estimators. We provide an implementation the proposed
estimators that show good performance in practice even for high dimensional
covariates.
