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The purpose of this article is to provide an adaptive estimator of thebaseline function in the Cox model with high-dimensional covariates. Weconsider a two-step procedure : first, we estimate the regression parameter ofthe Cox model via a Lasso procedure based on the partial log-likelihood,secondly, we plug this Lasso estimator into a least-squares type criterion andthen perform a model selection procedure to obtain an adaptive penalizedcontrast estimator of the baseline function. Using non-asymptotic estimationresults stated for the Lasso estimator of the regression parameter, weestablish a non-asymptotic oracle inequality for this penalized contrastestimator of the baseline function, which highlights the discrepancy of therate of convergence when the dimension of the covariates increases.

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