## The Annals of Statistics

### A Note on Convergence Rates for the Product Limit Estimator

#### 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

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