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

• 成果类型: Article
• 署名作者: Kim, Y; Lee, J
• 署名单位: Seoul National University (SNU)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000526
• 发表日期: 2004
• 页码: 1492-1512
• 关键词: posterior distributions; bayesian-analysis; LARGE-SAMPLE; Consistency; estimators; regression; CONVERGENCE; inference; rates

摘要

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 < 1/2, a prior process neutral to the right can be chosen so that its posterior distribution achieves the convergence rate n(-alpha).