Weak convergence results are proved for the product-limit estimator on the whole line. Applications are given to confidence band construction, estimation of mean lifetime, and to the theory of $q$-functions. The results are obtained using stochastic calculus and in probability linear bounds for empirical processes.
"Large Sample Behaviour of the Product-Limit Estimator on the Whole Line." Ann. Statist. 11 (1) 49 - 58, March, 1983. https://doi.org/10.1214/aos/1176346055