High-dimensional additive hazards models and the Lasso

We consider a general high-dimensional additive hazards model in a non-asymptotic setting, including regression for censored-data. In this context, we consider a Lasso estimator with a fully data-driven ℓ1 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.