On the bracketing entropy condition and generalized empirical measures

Davit Varron

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arXiv · 1609.07942

On the bracketing entropy condition and generalized empirical measures

Davit Varron

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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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Davit Varron. 2016-09-26. On the bracketing entropy condition and generalized empirical measures. https://arxiv.org/abs/1609.07942

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