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September, 1993 The Strong Law under Random Censorship
W. Stute, J.-L. Wang
Ann. Statist. 21(3): 1591-1607 (September, 1993). DOI: 10.1214/aos/1176349273

Abstract

Let $X_1, X_2, \ldots$ be a sequence of i.i.d. random variables with d.f. $F$. We observe $Z_i = \min(X_i,Y_i)$ and $\delta_i = 1_{\{X_i \leq Y_i\}}$, where $Y_1, Y_2, \ldots$ is a sequence of i.i.d. censoring random variables. Denote by $\hat{F}_n$ the Kaplan-Meier estimator of $F$. We show that for any $F$-integrable function $\varphi, \int\varphi d\hat{F}_n$ converges almost surely and in the mean. The result may be applied to yield consistency of many estimators under random censorship.

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W. Stute. J.-L. Wang. "The Strong Law under Random Censorship." Ann. Statist. 21 (3) 1591 - 1607, September, 1993. https://doi.org/10.1214/aos/1176349273

Information

Published: September, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0785.60020
MathSciNet: MR1241280
Digital Object Identifier: 10.1214/aos/1176349273

Subjects:
Primary: 60F15
Secondary: 60G42, 62G30

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 3 • September, 1993
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