HIGH DIMENSIONAL CENSORED QUANTILE REGRESSION.
HIGH DIMENSIONAL CENSORED QUANTILE REGRESSION.
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DOI：
10.1214/17-aos1551
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发表时间：
2018-03
影响因子：
4.5
通讯作者：
He X
中科院分区：
文献类型：
--
作者：
Zheng Q;Peng L;He X
截尾分位数回归 (CQR) 已成为生存分析的有用回归工具。一些常用的 CQR 方法可以通过跨分位数级别的顺序方式的基于随机积分的估计方程来表征。在本文中，我们在高维环境中分析 CQR，其中对连续分位数水平上的回归函数感兴趣。我们提出了一种两步惩罚程序，它适应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。我们为所提出的估计量建立了统一收敛率，并研究了弱收敛和变量选择的特性。我们进行数值研究以证实我们的理论发现并说明我们建议的实际效用。
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.