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

Agathe Guilloux 1 Sarah Lemler 2 Marie-Luce Taupin 2, 3, *
* Corresponding author
1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
3 MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas]
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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Journal articles
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https://hal.sorbonne-universite.fr/hal-01299325
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Submitted on : Thursday, April 7, 2016 - 2:52:31 PM
Last modification on : Thursday, March 21, 2019 - 2:54:17 PM

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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, 2016, 171, pp.38-62. ⟨10.1016/j.jspi.2015.11.005⟩. ⟨hal-01299325⟩

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