On the bracketing entropy condition and generalized empirical measures

2016/09/26 by Varron, Davit
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1609.07942

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

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