High-dimensional additive hazards models and the Lasso

Published in Electronic Journal of Statistics, 2012

S. Gaïffas and A. Guilloux

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 $\ell_1$-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.

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