Estimating a Monotone Density from Censored Observations
Huang, Youping ; Zhang, Cun-Hui
Ann. Statist., Tome 22 (1994) no. 1, p. 1256-1274 / Harvested from Project Euclid
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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.
Publié le : 1994-09-14
Classification:  Nonparametric maximum likelihood estimation,  censored data,  monotone density,  self-consistency,  least concave majorant,  product limit estimator,  62G05,  62G30,  62E20 
@article{1176325628,
     author = {Huang, Youping and Zhang, Cun-Hui},
     title = {Estimating a Monotone Density from Censored Observations},
     journal = {Ann. Statist.},
     volume = {22},
     number = {1},
     year = {1994},
     pages = { 1256-1274},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176325628}
}

Huang, Youping; Zhang, Cun-Hui. Estimating a Monotone Density from Censored Observations. Ann. Statist., Tome 22 (1994) no. 1, pp.  1256-1274. http://gdmltest.u-ga.fr/item/1176325628/