The Annals of Statistics

The Strong Law under Random Censorship

W. Stute and J.-L. Wang

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 21, Number 3 (1993), 1591-1607.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349273

Digital Object Identifier
doi:10.1214/aos/1176349273

Mathematical Reviews number (MathSciNet)
MR1241280

Zentralblatt MATH identifier
0785.60020

JSTOR
links.jstor.org

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

Keywords
Censored data SLLN reverse supermartingale Glivenko-Cantelli convergence

Citation

Stute, W.; Wang, J.-L. The Strong Law under Random Censorship. Ann. Statist. 21 (1993), no. 3, 1591--1607. doi:10.1214/aos/1176349273. https://projecteuclid.org/euclid.aos/1176349273.


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