On nonparametric hazard estimation.
The Nelson-Aalen estimator provides the basis for the ubiquitous Kaplan-Meier estimator, and therefore is an essential tool for nonparametric survival analysis. This article reviews martingale theory and its role in demonstrating that the Nelson-Aalen estimator is uniformly consistent for estimating the cumulative hazard function for right-censored continuous time-to-failure data.
Department of Biostatistics, University of Texas M.D. Anderson Cancer Center, Houston, TX, USA.
Brian P
BP
Hobbs
Asymptotic theory; Nelson-Aalen estimator; counting process; hazard estimation; martingale theory; time-to-failure analysis