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

Agathe Guilloux, Sarah Lemler and Marie-Luce Taupin

Journal of Multivariate Analysis, 2016, vol. 148, issue C, 141-159

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.

Keywords: Conditional hazard rate function; Semi-parametric model; Counting process; Kernel estimation; Goldenshluger and Lepski method; Non-asymptotic oracle inequality; Survival analysis (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:148:y:2016:i:c:p:141-159

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DOI: 10.1016/j.jmva.2016.03.002

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