Smooth backfitting of proportional hazards with multiplicative components

TL;DR

This paper extends smooth backfitting techniques to proportional hazards models with multiplicative components, providing asymptotic theory and practical in-sample forecasting improvements in survival analysis.

Contribution

It introduces smooth backfitting to survival analysis with multiplicative hazard components and develops asymptotic theory for the estimator.

Findings

Asymptotic properties of the estimator are established.

Enhanced in-sample forecasting methodology incorporating more information.

Practical application demonstrating the method's effectiveness.

Abstract

Smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression. Smooth backfitting projects the data down onto the structured space of interest providing a direct link between data and estimator. This paper introduces the ideas of smooth backfitting to survival analysis in a proportional hazard model, where we assume an underlying conditional hazard with multiplicative components. We develop asymptotic theory for the estimator and we use the smooth backfitter in a practical application, where we extend recent advances of in-sample forecasting methodology by allowing more information to be incorporated, while still obeying the structured requirements of in-sample forecasting.