The Annals of Statistics

The Central Limit Theorem Under Random Censorship

Winfried Stute

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Abstract

Let $\hat{F}_n$ be the Kaplan-Meier estimator of a distribution function $F$ computed from randomly censored data. We show that under optimal integrability assumptions on a function $\varphi$, the Kaplan-Meier integral $\int \varphi d\hat{F}_n$, when properly standardized, is asymptotically normal.

Article information

Source
Ann. Statist., Volume 23, Number 2 (1995), 422-439.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324528

Digital Object Identifier
doi:10.1214/aos/1176324528

Mathematical Reviews number (MathSciNet)
MR1332574

Zentralblatt MATH identifier
0829.62055

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 60G42: Martingales with discrete parameter 62G30: Order statistics; empirical distribution functions

Keywords
Censored data CLT Kaplan-Meier integral

Citation

Stute, Winfried. The Central Limit Theorem Under Random Censorship. Ann. Statist. 23 (1995), no. 2, 422--439. doi:10.1214/aos/1176324528. https://projecteuclid.org/euclid.aos/1176324528


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