In this note, we give a lemma which shows that the expected squared difference between the Bayes estimator with a Dirichlet process prior and the Kaplan-Meier product limit (PL) estimator for a survival function based on censored data is $O(n^{-2})$. This lemma, together with already proven pointwise consistency properties of the Bayes estimator, is used to establish two properties of the PL estimator; namely, the mean square consistency of the PL estimator with rate $O(n^{-1})$ and strong consistency of the PL estimator with rate $o(n^{-\frac{1}{2}} \log n)$.
Publié le : 1980-05-14
Classification:
Product limit estimator,
survival distribution,
Bayes estimator,
rates of convergence,
strong consistency,
mean square consistency,
censored data,
62G05,
60F99
@article{1176345017,
author = {Phadia, E. G. and Ryzin, J. Van},
title = {A Note on Convergence Rates for the Product Limit Estimator},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 673-678},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345017}
}
Phadia, E. G.; Ryzin, J. Van. A Note on Convergence Rates for the Product Limit Estimator. Ann. Statist., Tome 8 (1980) no. 1, pp. 673-678. http://gdmltest.u-ga.fr/item/1176345017/