Annals of Statistics

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

Yongdai Kim and Jaeyong Lee

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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

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

First available in Project Euclid: 4 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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