Edgeworth expansions are derived for a class of weighted bootstrap methods for the Kaplan-Meier and Nelson-Aalen estimates using the methods contained in the monograph by Barbe and Bertail. Von Mises representations up to the third order are established for the weighted bootstrap versions of these estimators. It is shown that there exists weights which outperform Efron's bootstrap method in terms of coverage accuracy. Moreover, it is shown that this holds for a particular choice of gamma weights which are very easy to use in practice. The general weighting schemes are also useful in approximating the posterior distribution of a survival function with respect to mixtures of beta-neutral process priors.
Lancelot F. James. "A study of a class of weighted bootstraps for censored data." Ann. Statist. 25 (4) 1595 - 1621, August 1997. https://doi.org/10.1214/aos/1031594733