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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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https://hal.archives-ouvertes.fr/hal-01171775
Contributor : Sarah Lemler <>
Submitted on : Wednesday, March 16, 2016 - 6:03:45 PM
Last modification on : Tuesday, March 17, 2020 - 2:11:04 AM

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  • HAL Id : hal-01171775, version 2
  • ARXIV : 1507.01397

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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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