BOOSTED NONPARAMETRIC HAZARDS WITH TIME-DEPENDENT COVARIATES

• 成果类型: Article
• 署名作者: Lee, Donald K. K.; Chen, Ningyuan; Ishwaran, Hemant
• 署名单位: Emory University; Emory University; University of Toronto; University of Miami
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS2028
• 发表日期: 2021
• 页码: 2101-2128
• 关键词: convergence; prediction; MODEL; regression

摘要

Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric loglikelihood functional and obtain its functional gradient. From this, we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard. The generic estimator is consistent if the model is correctly specified; alternatively, an oracle inequality can be demonstrated for tree-based models. To avoid overfitting, boosting employs several regularization devices. One of them is stepsize restriction, but the rationale for this is somewhat mysterious from the viewpoint of consistency. Our work brings some clarity to this issue by revealing that stepsize restriction is a mechanism for preventing the curvature of the risk from derailing convergence.