The Annals of Statistics

Estimation of Survival Curves from Dependent Censorship Models via a Generalized Self-Consistent Property with Nonparametric Bayesian Estimation Application

Wei-Yann Tsai

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 14, Number 1 (1986), 238-249.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349852

Digital Object Identifier
doi:10.1214/aos/1176349852

Mathematical Reviews number (MathSciNet)
MR829565

Zentralblatt MATH identifier
0596.62022

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G05: Estimation

Keywords
Generalized self-consistency survival function censored data Dirichlet process nonparametric Bayesian estimation dependent censorship models

Citation

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


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