Let $\hat{F}_n$ be the Kaplan-Meier estimator of a distribution function $F$ computed from randomly censored data. We show that under optimal integrability assumptions on a function $\varphi$, the Kaplan-Meier integral $\int \varphi d\hat{F}_n$, when properly standardized, is asymptotically normal.
@article{1176324528,
author = {Stute, Winfried},
title = {The Central Limit Theorem Under Random Censorship},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 422-439},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324528}
}
Stute, Winfried. The Central Limit Theorem Under Random Censorship. Ann. Statist., Tome 23 (1995) no. 6, pp. 422-439. http://gdmltest.u-ga.fr/item/1176324528/