On the Bernstein-von Mises theorem for the Dirichlet process

Ray, Kolyan; van der Vaart, Aad

doi:https://www.dx.doi.org/10.1214/21-EJS1821

File(s)

On the Bernstein-von Mises theorem.pdf (333.79 KB)

Published version

OA Location

https://arxiv.org/abs/2008.01130

Author(s)

Ray, Kolyan

van der Vaart, Aad

Type

Journal Article

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.

Date Issued

2021-04-16

Date Acceptance

2021-02-16

Citation

Electronic Journal of Statistics, 2021, 15 (1), pp.2224-2246

URI

http://hdl.handle.net/10044/1/88096

URL

https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-1/On-the-Bernstein-von-Mises-theorem-for-the-Dirichlet-process/10.1214/21-EJS1821.full

DOI

https://www.dx.doi.org/10.1214/21-EJS1821

ISSN

1935-7524

Publisher

Institute of Mathematical Statistics

Start Page

2224

End Page

2246

Journal / Book Title

Electronic Journal of Statistics

Volume

15

Issue

1

Copyright Statement

License URL

https://creativecommons.org/licenses/by/4.0/

Identifier

https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-1/On-the-Bernstein-von-Mises-theorem-for-the-Dirichlet-process/10.1214/21-EJS1821.full

Subjects

0104 Statistics

Publication Status

Published

Date Publish Online

2021-04-16