In this paper we consider the product-limit estimator of the survival distribution function in the context of independent but nonidentically distributed censoring times. An upper bound on the mean square increment of the stopped Kaplan-Meier process is obtained. Also, a representation is given for the ratio of the survival distribution function to the product-limit estimator as the product of a bounded process and a martingale. From this representation bounds on the mean square of the ratio and on the tail probability of the sup norm of the ratio are derived.
Publié le : 1992-03-14
Classification:
Product-limit estimator,
martingale,
Volterra integral equation,
Gronwall's inequality,
62E20,
62G99,
62M99
@article{1176348537,
author = {Yang, Song},
title = {Some Inequalities About the Kaplan-Meier Estimator},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 535-544},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348537}
}
Yang, Song. Some Inequalities About the Kaplan-Meier Estimator. Ann. Statist., Tome 20 (1992) no. 1, pp. 535-544. http://gdmltest.u-ga.fr/item/1176348537/