Open Access
August 2004 A Bernstein–von Mises theorem in the nonparametric right-censoring model
Yongdai Kim, Jaeyong Lee
Ann. Statist. 32(4): 1492-1512 (August 2004). DOI: 10.1214/009053604000000526


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.


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Yongdai Kim. Jaeyong Lee. "A Bernstein–von Mises theorem in the nonparametric right-censoring model." Ann. Statist. 32 (4) 1492 - 1512, August 2004.


Published: August 2004
First available in Project Euclid: 4 August 2004

zbMATH: 1047.62043
MathSciNet: MR2089131
Digital Object Identifier: 10.1214/009053604000000526

Primary: 62C10
Secondary: 62G20 , 62N01

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

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 4 • August 2004
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