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May, 1980 A Note on Convergence Rates for the Product Limit Estimator
E. G. Phadia, J. Van Ryzin
Ann. Statist. 8(3): 673-678 (May, 1980). DOI: 10.1214/aos/1176345017

Abstract

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 $o(n^{-\frac{1}{2}} \log n)$.

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E. G. Phadia. J. Van Ryzin. "A Note on Convergence Rates for the Product Limit Estimator." Ann. Statist. 8 (3) 673 - 678, May, 1980. https://doi.org/10.1214/aos/1176345017

Information

Published: May, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0461.62040
MathSciNet: MR568729
Digital Object Identifier: 10.1214/aos/1176345017

Subjects:
Primary: 62G05
Secondary: 60F99

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 3 • May, 1980
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