Functional central limit theorems for the Nelson–Aalen and Kaplan–Meier estimators for dependent stationary data

Abstract

We derive process limit distribution results for the Nelson–Aalen estimator of a hazard function and for the Kaplan–Meier estimator of a distribution function, under different dependence assumptions. The data are assumed to be right censored observations of a stationary time series. We treat weakly dependent as well as long range dependent data, and allow for qualitative differences in the dependence for the censoring times versus the time of interest.