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December, 1987 Strong Consistency of a Nonparametric Estimator of the Survival Function with Doubly Censored Data
Myron N. Chang, Grace L. Yang
Ann. Statist. 15(4): 1536-1547 (December, 1987). DOI: 10.1214/aos/1176350608

Abstract

A double censoring mechanism is such that each variable $X$ in the sample is observable if and only if $X$ is within the observation interval $\lbrack Z, Y \rbrack$. Otherwise, we can only determine whether $X$ is less than $Z$ or greater than $Y$ and observe $Z$ or $Y$ correspondingly. This kind of censoring occurs often in collecting lifetime data. Our problem is to estimate the survival function of $X, S_X(t) = P \lbrack X > t \rbrack$, from a doubly censored sample, where $X$ is assumed to be independent of the random interval $\lbrack Z, Y \rbrack$. We establish sufficient conditions for which $S_X(t)$ is identifiable and then prove the strong consistency of the self-consistent estimator $\hat{S}_X(t)$ for $S_X(t)$. This investigation generalizes the results available for the right censored data.

Citation

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Myron N. Chang. Grace L. Yang. "Strong Consistency of a Nonparametric Estimator of the Survival Function with Doubly Censored Data." Ann. Statist. 15 (4) 1536 - 1547, December, 1987. https://doi.org/10.1214/aos/1176350608

Information

Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0629.62040
MathSciNet: MR913572
Digital Object Identifier: 10.1214/aos/1176350608

Subjects:
Primary: 62G05
Secondary: 62G99

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 4 • December, 1987
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