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 $p \geq 2$. In particular, we obtain what we conjecture to be the asymptotically optimal rate whenever the density of the summands admits a non-zero continuous component and has a non-zero third moment.