TITLE:
Asymptotic Normality of the Nelson-Aalen and the Kaplan-Meier Estimators in Competing Risks
AUTHORS:
Didier Alain Njamen Njomen
KEYWORDS:
Censored Data, Right-Censoring, Counting Process, Competing Risks, Nelson-Aalen and Kaplan-Meier Estimators, Asymptotic Properties of Estimators, Confidence Bands
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.7,
July
22,
2019
ABSTRACT: This paper studies the asymptotic normality of the Nelson-Aalen and the Kaplan-Meier estimators in a competing risks context in presence of independent right-censorship. To prove our results, we use Robelledo’s theorem which makes it possible to apply the central limit theorem to certain types of particular martingales. From the results obtained, confidence bounds for the hazard and the survival functions are provided.