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Journal Articles Journal of Multivariate Analysis Year : 2016

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

Abstract

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.

Dates and versions

hal-01327412 , version 1 (06-06-2016)

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Cite

Agathe Guilloux, Sarah Lemler, Marie-Luce Taupin. Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates. Journal of Multivariate Analysis, 2016, 148, pp.141-159. ⟨10.1016/j.jmva.2016.03.002⟩. ⟨hal-01327412⟩
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