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

doi:10.1016/j.jspi.2015.11.005

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, *}

* Auteur correspondant

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.

Type de document :

Article dans une revue

Journal of Statistical Planning and Inference, Elsevier, 2016, 171, pp.38-62. 〈10.1016/j.jspi.2015.11.005〉

Domaine :

Mathématiques [math] / Statistiques [math.ST]

Liste complète des métadonnées

https://hal.sorbonne-universite.fr/hal-01299325
Contributeur : Gestionnaire Hal-Upmc <>
Soumis le : jeudi 7 avril 2016 - 14:52:31
Dernière modification le : jeudi 21 mars 2019 - 14:54:17

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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