City Research Online

Abstract

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 propose an implementation of estimators that show good performance in practice.

Publication Type:	Article
Additional Information:	This is the peer reviewed version of the following article: Bishopberger, S., Hiabu, M., Mammen, E. & Perch Nielsen, J. (2025). Smooth Backfitting for Additive Hazard Rates. Scandinavian Journal of Statistics, which will be published in final form at onlinelibrary.wiley.com/journal/14679469. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
Publisher Keywords:	additive hazard model; local linear kernel estimation; smooth backfitting; survival analysis
Subjects:	H Social Sciences > HG Finance
Departments:	Bayes Business School Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:	Symplectic Administrator

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