On the Bernstein-von Mises theorem for the Dirichlet process
Statistics Theory
2022-10-10 v2 Probability
Statistics Theory
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.
Cite
@article{arxiv.2008.01130,
title = {On the Bernstein-von Mises theorem for the Dirichlet process},
author = {Kolyan Ray and Aad van der Vaart},
journal= {arXiv preprint arXiv:2008.01130},
year = {2022}
}