Zheng Qi, Peng Limin, He Xuming
Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, KY 40242, USA.
Department of Biostatistics and Bioinformatics, Emory University, 1518 Clifton Rd, NE, Atlanta, GA 30322, USA.
Ann Stat. 2018 Feb;46(1):308-343. doi: 10.1214/17-AOS1551. Epub 2018 Feb 22.
Censored quantile regression (CQR) has emerged as a useful regression tool for survival analysis. Some commonly used CQR methods can be characterized by stochastic integral-based estimating equations in a sequential manner across quantile levels. In this paper, we analyze CQR in a high dimensional setting where the regression functions over a continuum of quantile levels are of interest. We propose a two-step penalization procedure, which accommodates stochastic integral based estimating equations and address the challenges due to the recursive nature of the procedure. We establish the uniform convergence rates for the proposed estimators, and investigate the properties on weak convergence and variable selection. We conduct numerical studies to confirm our theoretical findings and illustrate the practical utility of our proposals.
删失分位数回归（CQR）已成为生存分析中一种有用的回归工具。一些常用的CQR方法可以通过基于随机积分的估计方程，以分位数水平的顺序方式进行刻画。在本文中，我们在高维环境下分析CQR，其中连续分位数水平上的回归函数是我们感兴趣的。我们提出了一种两步惩罚程序，该程序适用于基于随机积分的估计方程，并解决了由于该程序的递归性质而带来的挑战。我们建立了所提出估计量的一致收敛速度，并研究了弱收敛和变量选择的性质。我们进行了数值研究以证实我们的理论发现，并说明了我们提议的实际效用。
