High dimensional censored quantile regression
针对生存分析中高维删失数据，提出两步惩罚方法处理随机积分估计方程，证明估计量的一致收敛速率和变量选择性质，并通过数值实验验证。
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.