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

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

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.

Document type :

Journal articles

Domain :

Mathematics [math] / Statistics [math.ST]

Complete list of metadatas

https://hal.sorbonne-universite.fr/hal-01299325
Contributor : Gestionnaire Hal-Upmc <>
Submitted on : Thursday, April 7, 2016 - 2:52:31 PM
Last modification on : Thursday, March 21, 2019 - 2:54:17 PM

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

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

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