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Asymptotic Normality of the Nelson-Aalen and the Kaplan-Meier Estimators in Competing Risks
Department of Mathematics and Computer Science, Faculty of Science, University of Maroua, Maroua, Cameroon
- 1 Department of Mathematics and Computer Science, Faculty of Science, University of Maroua, Maroua, Cameroon
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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.
KeywordsCensored DataRight-CensoringCounting ProcessCompeting RisksNelson-Aalen and Kaplan-Meier EstimatorsAsymptotic Properties of EstimatorsConfidence Bands
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