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

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.
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https://hal.archives-ouvertes.fr/hal-01120683
Contributor : Sarah Lemler <>
Submitted on : Sunday, March 1, 2015 - 10:06:51 PM
Last modification on : Friday, June 19, 2020 - 1:02:54 PM
Document(s) archivé(s) le : Tuesday, June 2, 2015 - 9:31:03 AM

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Agathe Guilloux, Sarah Lemler, Marie-Luce Taupin. Adaptive estimation of the baseline hazard function in the Cox model by model selection, with high-dimensional covariates. Journal of Statistical Planning and Inference, Elsevier, 2015, 171, pp.38-62. ⟨10.1016/j.jspi.2015.11.005⟩. ⟨hal-01120683v2⟩

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