On the Bernstein-von Mises theorem for the Dirichlet process

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.

References in corpus (3)

• Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions
• Large sample asymptotics for the two-parameter Poisson--Dirichlet process
• Semiparametric Bayesian causal inference

Cited by in corpus (2)

• Semiparametric Bayesian causal inference
• Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime