Consistency of the Kaplan-Meier Estimator of the Survival Function in Competiting Risks

Didier Alain Njamen Njomen () and Joseph Wandji Ngatchou
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Didier Alain Njamen Njomen: Department of Mathematics and Computer Sciences, Faculty of Science, University of Maroua, Maroua, Cameroon
Joseph Wandji Ngatchou: Institut Elie Cartan de Lorraine, University of Lorraine, Nancy, France

The Open Statistics and Probability Journal, 2018, vol. 9, issue 1, 1-17

Abstract: Introduction : In this article, we only focus on the probability distributions of the breakdown time whose causes are known, and we consider a partition of the observations into subgroups according to each of the causes as defined in Njamen and Ngatchou [1]. By adapting the stochastic processes developed by Aalen [2, 3], we derive a Kaplan-Meier [4] nonparametric estimator for the survival function in competiting risks. Result & Discussion : In a region where there is at least one observation, we prove on one hand that this new nonparametric estimator is unbiased in competiting risk and on the other hand, using the Lenglart inequality, we establish its uniform consistency in competiting risks.

Keywords: Censored data; Counting process; Survival function; Competiting risks; Kaplan-Meier estimators; Bias of an estimator; Uniform consistency. (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:ben:tostpj:v:9:y:2018:i:1:p:1-17

DOI: 10.2174/1876527001809010001

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