Quantitative Multidimensional Central Limit Theorems for Means of the Dirichlet-Ferguson Measure

The Dirichlet-Ferguson measure is a cornerstone in nonparametric Bayesian statistics and the study of distributional properties of expectations with respect to such measure is an important line of research. In this paper we provide explicit upper bounds for the d2, the d3 and the convex distance between vectors whose components are means of the Dirichlet-Ferguson measure and a Gaussian random vector.