Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates

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• 作者：Agathe Guilloux^a ; ^b ; ^{agathe.guilloux@upmc.fr" class="auth_mail" title="E-mail the corresponding author} ; Sarah Lemler^c ; ^{sarah.lemler@centralesupelec.fr" class="auth_mail" title="E-mail the corresponding author} ; Marie-Luce Taupin^d ; ^e ; ^{marie-luce.taupin@genopole.cnrs.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62G05 ; 62G08 ; 62N01 ; 62N02 ; 62P10 ; 62H12
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：148
• 期：Complete
• 页码：141-159
• 全文大小：583 K

文摘

We propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a LASSO procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Breslow estimator of the cumulative baseline function. We propose and study an adaptive procedure for selecting the bandwidth, in the spirit of Goldenshluger and Lepski (2011). We state non-asymptotic oracle inequalities for the final estimator, which leads to a reduction in the rate of convergence when the dimension of the covariates grows.