The Strong Law under Random Censorship
Stute, W. ; Wang, J.-L.
Ann. Statist., Tome 21 (1993) no. 1, p. 1591-1607 / Harvested from Project Euclid
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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.
Publié le : 1993-09-14
Classification:  Censored data,  SLLN,  reverse supermartingale,  Glivenko-Cantelli convergence,  60F15,  60G42,  62G30 
@article{1176349273,
     author = {Stute, W. and Wang, J.-L.},
     title = {The Strong Law under Random Censorship},
     journal = {Ann. Statist.},
     volume = {21},
     number = {1},
     year = {1993},
     pages = { 1591-1607},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176349273}
}

Stute, W.; Wang, J.-L. The Strong Law under Random Censorship. Ann. Statist., Tome 21 (1993) no. 1, pp.  1591-1607. http://gdmltest.u-ga.fr/item/1176349273/