The Annals of Statistics
- Ann. Statist.
- Volume 22, Number 3 (1994), 1256-1274.
Estimating a Monotone Density from Censored Observations
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.
Ann. Statist., Volume 22, Number 3 (1994), 1256-1274.
First available in Project Euclid: 11 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G05: Estimation
Secondary: 62G30: Order statistics; empirical distribution functions 62E20: Asymptotic distribution theory
Huang, Youping; Zhang, Cun-Hui. Estimating a Monotone Density from Censored Observations. Ann. Statist. 22 (1994), no. 3, 1256--1274. doi:10.1214/aos/1176325628. https://projecteuclid.org/euclid.aos/1176325628