ESTIMATING A MONOTONE DENSITY FROM CENSORED OBSERVATIONS

• 成果类型: Article
• 署名作者: HUANG, YP; ZHANG, CH
• 署名单位: Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325628
• 发表日期: 1994
• 页码: 1256-1274
• 关键词: large sample; product

摘要

We study the nonparametric maximum likelihood estimator (NPMLE) for a concave distribution function F and its decreasing density f based on right-censored data. Without the concavity constraint, the NPMLE of F is the product-limit estimator proposed by Kaplan and Meier. If there is no censoring, the NPMLE of f, derived by Grenander, is the left derivative of the least concave majorant of the empirical distribution function, and its local and global behavior was investigated, respectively, by Prakasa Rao and Groeneboom. In this paper, we present a necessary and sufficient condition, a self-consistency equation and an analytic solution for the NPMLE, and we extend Prakasa Rao's result to the censored model.