On the bracketing entropy condition and generalized empirical measures
Statistics Theory
2016-09-27 v1 Statistics Theory
Abstract
We prove a Donsker and a Glivenko--Cantelli theorem for sequences of random discrete measures generalizing empirical measures. Those two results hold under standard conditions upon bracketing numbers of the indexing class of functions. As a byproduct, we derive a posterior consistency and a Bernstein--von Mises theorem for the Dirichlet process prior, under the topology of total variation, when the observation space is countable. We also obtain new information about the Durst--Dudley--Borisov theorem
Cite
@article{arxiv.1609.07942,
title = {On the bracketing entropy condition and generalized empirical measures},
author = {Davit Varron},
journal= {arXiv preprint arXiv:1609.07942},
year = {2016}
}