The Annals of Statistics
- Ann. Statist.
- Volume 14, Number 1 (1986), 238-249.
Estimation of Survival Curves from Dependent Censorship Models via a Generalized Self-Consistent Property with Nonparametric Bayesian Estimation Application
This article presents a family of estimators of the survival function based on right-censored observations which admit the possibility that the censoring variables may not be independent of the true failure variables. This family is obtained by generalizing the self-consistent property (Efron, 1967) of the product limit estimator (Kaplan and Meier, 1958). By assuming a Dirichlet process prior distribution of the observable random vectors, nonparametric Bayesian estimators of the survival curve-which is also a member of this family--are derived under a special loss function. These nonparametric Bayesian estimators generalize results of Susarla and Van Ryzin (1976), who impose a Dirichlet process prior on the failure survival function without considering any prior distribution of the censoring variables. Large sample properties of this family of nonparametric Bayesian estimators are also derived.
Ann. Statist., Volume 14, Number 1 (1986), 238-249.
First available in Project Euclid: 12 April 2007
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Tsai, Wei-Yann. Estimation of Survival Curves from Dependent Censorship Models via a Generalized Self-Consistent Property with Nonparametric Bayesian Estimation Application. Ann. Statist. 14 (1986), no. 1, 238--249. doi:10.1214/aos/1176349852. https://projecteuclid.org/euclid.aos/1176349852