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Adaptive estimation of the baseline hazard function in the Cox model by model selection, with high-dimensional covariates

Research paper by Agathe Guilloux, Sarah Lemler, Marie-Luce Taupin

Indexed on: 03 Mar '15Published on: 03 Mar '15Published in: Mathematics - Statistics



Abstract

The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via a Lasso procedure based on the partial log-likelihood, secondly, we plug this Lasso estimator into a least-squares type criterion and then perform a model selection procedure to obtain an adaptive penalized contrast estimator of the baseline function. Using non-asymptotic estimation results stated for the Lasso estimator of the regression parameter, we establish a non-asymptotic oracle inequality for this penalized contrast estimator of the baseline function, which highlights the discrepancy of the rate of convergence when the dimension of the covariates increases.