The kernel estimator is a widely used tool for the estimation of a density function. In this paper its adaptation to censored data using the Kaplan-Meier estimator is considered. Asymptotic properties of four estimators, arising naturally as a result of considering various types of bandwidths, are investigated. In particular we show that (i) both proposed estimators stemming from the nearest neighbor estimator have censoring-free variances and (ii) one of them is pointwise mean consistent.
Publié le : 1986-06-14
Classification:
Censored data,
density estimator,
$k$ nearest neighbor estimator,
Kaplan-Meier estimator,
kernel,
random censorship model,
62G05,
60F15
@article{1176349954,
author = {Mielniczuk, Jan},
title = {Some Asymptotic Properties of Kernel Estimators of a Density Function in Case of Censored Data},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 766-773},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349954}
}
Mielniczuk, Jan. Some Asymptotic Properties of Kernel Estimators of a Density Function in Case of Censored Data. Ann. Statist., Tome 14 (1986) no. 2, pp. 766-773. http://gdmltest.u-ga.fr/item/1176349954/