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.
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https://hal.sorbonne-universite.fr/hal-01327412
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Submitted on : Monday, June 6, 2016 - 4:54:33 PM
Last modification on : Thursday, March 28, 2019 - 4:16:18 AM

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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, Elsevier, 2016, 148, pp.141-159. ⟨10.1016/j.jmva.2016.03.002⟩. ⟨hal-01327412⟩

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