The Annals of Statistics

A Note on Convergence Rates for the Product Limit Estimator

E. G. Phadia and J. Van Ryzin

Full-text: Open access

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

Article information

Source
Ann. Statist., Volume 8, Number 3 (1980), 673-678.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345017

Digital Object Identifier
doi:10.1214/aos/1176345017

Mathematical Reviews number (MathSciNet)
MR568729

Zentralblatt MATH identifier
0461.62040

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 60F99: None of the above, but in this section

Keywords
Product limit estimator survival distribution Bayes estimator rates of convergence strong consistency mean square consistency censored data

Citation

Phadia, E. G.; Ryzin, J. Van. A Note on Convergence Rates for the Product Limit Estimator. Ann. Statist. 8 (1980), no. 3, 673--678. doi:10.1214/aos/1176345017. https://projecteuclid.org/euclid.aos/1176345017


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