B0345
Title: Donsker and Glivenko-Cantelli theorems for a class of processes generalizing the empirical process
Authors: Davit Varron - University of Franche-Comte (France) [presenting]
Abstract: The aim is to present a general limit theorem for sequences of random discrete probability measures for which the structural assumption is that the point masses are conditionally i.i.d. given the weights. Such a class of random discrete measures not only encompasses the empirical measure, but also encompasses the normalised homogenous completely random measures, stick breaking random measures (or priors). We shall state a Donsker and a Glivenko Cantelli theorem for thoses radom measures, as processes indexed by a class of functions admitting a uniform entropy integral. As a by product of our results, we will provide an alternative proof of the posterior consistency and the Bernstein von Mises phenomenon (in strong topologies) of the Dirichlet process prior.
