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.
翻译:平滑的回缩最初是在一种添加式回归环境中通过直接投影替代Buja、Hastie和Tibshirani的经典回缩方法的替代物引入的。 本文将原来的平滑回缩概念转换成一个生存模型, 以考虑到一种添加式结构的危险。 该模型允许在医学研究或精算保留等许多应用中出现检查和脱轨模式。 我们的估测器被证明是将数据投入带有平滑添加剂成分的多变量危险功能的空间。 因此, 我们的危害估计器是最接近的非参数添加剂, 即使实际危险率不是添加剂。 这不同于其他添加式结构估测器, 如果模型不正确, 则无法做出估计。 我们为我们的估测器提供完整的反射理论。 我们提供一个实施建议中的估测器, 显示即使在高维变量中, 也实际表现良好。