Almost sure asymptotic representation for a class of functionals of the Kaplan-Meier estimator

Abstract

This paper deals with censored data estimation of a general class of von Mises-type functionals of the survival time distribution $F$. Conditions are given under which an almost sure asymptotic representation holds for the estimator, obtained by applying the same functional to $\hat{F}_n$, the product-limit estimator of Kaplan and Meier.