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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 [14]. 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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Dates and versions

hal-01171775 , version 1 (06-07-2015)
hal-01171775 , version 2 (16-03-2016)

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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. 2015. ⟨hal-01171775v2⟩
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