A bias-corrected Nelson-Aalen estimator

Abstract

The starting point to model an incomplete dataset of a non-negative random variable is usually to estimate its reliability function using a non-parametric reliability estimator. Two such estimators are Kaplan-Meier estimator and Nelson-Aalen estimator. Their performances have been compared and some drawbacks (e.g., biasness) have been identified in the literature. However, improvements on them are scarce. This paper aims to fill this gap by proposing a simple and almost unbiased estimator. This estimator is a weighted average of the Nelson-Aalen reliability estimates at two successive time points. An application of the proposed estimator in model selection is discussed and a real-world dataset is analyzed to illustrate the appropriateness and usefulness of the proposed estimator.