On the Bernstein-von Mises theorem for the Dirichlet process

Electronic Journal of Statistics, vol. 15

Abstract

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.

Authors 2

1. Kolyan Ray

   Imperial College London

   Affiliation as printed

   Department of Mathematics, Imperial College London, United Kingdom

   Imperial College London

2. Aad van der Vaart Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, Netherlands

   Leiden University