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

TL;DR

This paper establishes functional central limit theorems for Nelson-Aalen and Kaplan-Meier estimators when applied to dependent stationary data, including weakly and long-range dependent cases, with different dependence structures for censoring and event times.

Contribution

It extends the theoretical understanding of these estimators by deriving their limit distributions under various dependence assumptions in stationary time series.

Findings

Limit distribution results for Nelson-Aalen estimator under dependence

Limit distribution results for Kaplan-Meier estimator under dependence

Handles both weak and long-range dependence with different censoring structures

Abstract

We derive process limit distribution results for the Nelson-Aalen estimator of a hasard 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