High-dimensional additive hazard models and the Lasso

TL;DR

This paper develops a Lasso-based estimator for high-dimensional additive hazard models with censored data, providing sharp oracle inequalities and introducing a novel data-driven Bernstein's inequality.

Contribution

It introduces a fully data-driven Lasso estimator for high-dimensional additive hazard models and proves sharp oracle inequalities for its performance.

Findings

The estimator achieves sharp oracle inequalities.

A new data-driven Bernstein's inequality is developed.

The method effectively handles censored data in high dimensions.

Abstract

We consider a general high-dimensional additive hazard model in a non-asymptotic setting, including regression for censored-data. In this context, we consider a Lasso estimator with a fully data-driven $\ell_1$ penalization, which is tuned for the estimation problem at hand. We prove sharp oracle inequalities for this estimator. Our analysis involves a new "data-driven" Bernstein's inequality, that is of independent interest, where the predictable variation is replaced by the optional variation.