On the weak convergence of certain estimators of stochastically ordered survival functions

This is the authors' abstract. We don't add key points for this paper.

Let F and G be distribution functions with corresponding survival functions . When is known and for all x, the estimator where represents the empirical survival function, has been considered by Rojo and Ma. In the two-sample problem when both are unknown with for all x, Lo and Rojo and Ma have considered the estimators and where represent the empirical survival functions based on random samples from F and G of sizes n and m respectively. Here, the weak convergence of is considered. It is shown, under mild conditions on F and G, that and converge weakly when for all x. However, when for some x0, weak convergence doesnot hold. Similar results are obtained in the case of censored data by replacing the empirical survival functions by their Kaplan-Meier counterparts. The estimators are illustrated with some examples from engineering and the biomedical sciences.