Improved rates of convergence for the multivariate Central Limit Theorem in Wasserstein distance

Abstract

We provide new bounds for the rate of convergence of the multivariate Central Limit Theorem in Wasserstein distances of order $p\ge 2$. In particular, we obtain what we conjecture to be the asymptotically optimal rate in the identically distributed case whenever the measure of the summands admits a non-zero continuous component and has a non-zero third moment.