The Annals of Statistics

A Bernstein–von Mises theorem in the nonparametric right-censoring model

Yongdai Kim and Jaeyong Lee

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Abstract

In the recent Bayesian nonparametric literature, many examples have been reported in which Bayesian estimators and posterior distributions do not achieve the optimal convergence rate, indicating that the Bernstein–von Mises theorem does not hold. In this article, we give a positive result in this direction by showing that the Bernstein–von Mises theorem holds in survival models for a large class of prior processes neutral to the right. We also show that, for an arbitrarily given convergence rate n−α with 0<α≤1/2, a prior process neutral to the right can be chosen so that its posterior distribution achieves the convergence rate n−α.

Article information

Source
Ann. Statist., Volume 32, Number 4 (2004), 1492-1512.

Dates
First available in Project Euclid: 4 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1091626176

Digital Object Identifier
doi:10.1214/009053604000000526

Mathematical Reviews number (MathSciNet)
MR2089131

Zentralblatt MATH identifier
1047.62043

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62G20: Asymptotic properties 62N01: Censored data models

Keywords
Bernstein–von Mises theorem neutral to the right process survival model

Citation

Kim, Yongdai; Lee, Jaeyong. A Bernstein–von Mises theorem in the nonparametric right-censoring model. Ann. Statist. 32 (2004), no. 4, 1492--1512. doi:10.1214/009053604000000526. https://projecteuclid.org/euclid.aos/1091626176


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