In this paper the asymptotic behaviour of the product limit estimator $F_n$ of an unknown distribution is investigated. We give an approximation of the difference $F_n(x) - F(x)$ by a Gaussian process and also by the average of i.i.d. processes. We get almost as good an approximation of the stochastic process $F_n(x) - F(x)$ as one can get for the analogous problem when the maximum likelihood estimator is approximated by a Gaussian random variable or by the average of i.i.d. random variables in the parametric case.
@article{1176350949,
author = {Major, P. and Rejto, L.},
title = {Strong Embedding of the Estimator of the Distribution Function under Random Censorship},
journal = {Ann. Statist.},
volume = {16},
number = {1},
year = {1988},
pages = { 1113-1132},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350949}
}
Major, P.; Rejto, L. Strong Embedding of the Estimator of the Distribution Function under Random Censorship. Ann. Statist., Tome 16 (1988) no. 1, pp. 1113-1132. http://gdmltest.u-ga.fr/item/1176350949/