标题： Cox模型中基线函数的自适应核估计，具有高维协变量 显示英文标题

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

摘要： 本文的目的是提出一种一般高维Cox模型中基线函数的新核估计量，并推导出非渐近收敛速率。 为了构造我们的估计量，我们首先通过Lasso过程估计Cox模型中的回归参数。 然后我们将该估计量代入经典的基线函数核估计量中，该估计量是通过平滑所谓的Breslow估计量的累积基线函数得到的。 我们提出并研究了一种自适应的带宽选择过程，其思想源于Goldenshluger和Lepski（2011）。 我们给出了最终估计量的非渐近Oracle不等式，这些不等式揭示了当协变量维度增长时收敛速率的降低。 显示英文摘要

摘要： 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.