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

TL;DR

This paper introduces an adaptive kernel estimator for the baseline function in high-dimensional Cox models, combining Lasso-based parameter estimation with a novel bandwidth selection method, and provides theoretical convergence guarantees.

Contribution

It presents a new kernel estimator for the baseline function in high-dimensional Cox models, incorporating adaptive bandwidth selection and non-asymptotic convergence analysis.

Findings

Non-asymptotic convergence rates derived

Bandwidth selection improves estimator performance

Rates decrease as covariate dimension increases

Abstract

The aim of this article is to 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 Gold-enshluger and Lepski (2011). We state non-asymptotic oracle inequalities for the final estimator, which reveal the reduction of the rates of convergence when the dimension of the covariates grows.