On the bracketing entropy condition and generalized empirical measures
Davit Varron · Latin American Journal of Probability and Mathematical Statistics · 2025
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 insights upon the Durst-Dudley-Borisov theorem