文章基本信息

标题：On the Bernstein-von Mises theorem for the Dirichlet process
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作者：Kolyan Ray ; Aad van der Vaart
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2021
卷号：15
期号：1
页码：2224-2246
DOI：10.1214/21-EJS1821
语种：English
出版社：Institute of Mathematical Statistics
摘要：We establish that Laplace transforms of the posterior Dirichlet process converge to those of the limiting Brownian bridge process in a neighbourhood about zero, uniformly over Glivenko-Cantelli function classes. For real-valued random variables and functions of bounded variation, we strengthen this result to hold for all real numbers. This last result is proved via an explicit strong approximation coupling inequality.
关键词：60F17; 62G15; 62G20; Bayesian nonparametrics; Bernstein–Von Mises; Dirichlet process; strong approximation