ESTIMATING A MONOTONE DENSITY FROM CENSORED OBSERVATIONS
ESTIMATING A MONOTONE DENSITY FROM CENSORED OBSERVATIONS
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DOI：
10.1214/aos/1176325628
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发表时间：
1994-09-01
影响因子：
4.5
通讯作者：
ZHANG, CH
中科院分区：
文献类型：
--
作者：
HUANG, YP;ZHANG, CH
研究了右删失数据下凹分布函数F及其递减密度f的非参数极大似然估计。在没有凹性约束的情况下，F的NPMLE是Kaplan和Meier提出的乘积极限估计。在没有截尾的情况下，由Griander导出的f的NPMLE是经验分布函数的最小凹多数的左导数，Prakasa Rao和Groeneom分别研究了它的局部和全局行为。本文给出了NPMLE的充要条件、自洽方程和解析解，并将Prakasa Rao的结果推广到删失模型。
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.