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

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

2004-10-05

arxiv.org/abs/math/0410083v1

Annals of Statistics 2004, Vol. 32, No. 4, 1492-1512

Mathematics

Statistics Theory

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat

Scientific paper

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^{-\alpha} with 0<\alpha \leq 1/2, a prior process neutral to the right can be chosen so that its posterior distribution achieves the convergence rate n^{-\alpha}.

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