SCALABLE ESTIMATION AND INFERENCE FOR CENSORED QUANTILE REGRESSION PROCESS

• 成果类型: Article
• 署名作者: He, Xuming; Pan, Xiaoou; Tan, Kean Ming; Zhou, Wen-Xin
• 署名单位: University of Michigan System; University of Michigan; University of California System; University of California San Diego
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2214
• 发表日期: 2022
• 页码: 2899-2924
• 关键词: nonconcave penalized likelihood; proportional hazards model; variable selection; regularized estimation; estimating equations; survival analysis; resampling method

摘要

Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge for large-scale data with many covariates. In this paper, we focus on a smoothed martingale-based sequential estimating equations approach, to which scalable gradient-based algorithms can be applied. Theoretically, we provide a unified analysis of the smoothed sequential estimator and its penalized counterpart in increasing dimensions. When the covariate dimension grows with the sample size at a sublinear rate, we establish the uniform convergence rate (over a range of quantile indexes) and provide a rigorous justification for the validity of a multiplier bootstrap procedure for inference. In high-dimensional sparse settings, our results considerably improve the existing work on CQR by relaxing an exponential term of sparsity. We also demonstrate the advantage of the smoothed CQR over existing methods with both simulated experiments and data applications.