Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications

• 成果类型: Article
• 署名作者: Deheuvels, P; Einmahl, JH
• 署名单位: Sorbonne Universite; Eindhoven University of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 1301-1335
• 关键词: local empirical processes; hazard rate estimation; iterated logarithm; random censorship; quantile processes; Gaussian Approximation; density estimators; kernel estimators; BEHAVIOR; REPRESENTATIONS

摘要

We prove functional limit laws for the increment functions of empirical processes based upon randomly right-censored data. The increment sizes we consider are classified into different classes covering the whole possible spectrum. We apply these results to obtain a description of the strong limiting behavior of a series of estimators of local functionals of lifetime distributions. In particular, we treat the case of kernel density and hazard rate estimators.