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.
"Strong Embedding of the Estimator of the Distribution Function under Random Censorship." Ann. Statist. 16 (3) 1113 - 1132, September, 1988. https://doi.org/10.1214/aos/1176350949