Improved rates of convergence for the multivariate central limit theorem in Wasserstein distance (Q6595693)

Let \(W_1,\ldots,W_n\) be independent and centred random variables on \(\mathbb{R}^d\), and \(W=W_1+\cdots+W_n\) their sum having an identity covariance matrix. The author establishes new bounds in the multivariate central limit theorem for \(W\) in Wasserstein distance of order \(p\geq2\) which improve on the rates available in the literature. The author conjectures that this rate is optimal in the case where the \(W_i\) are identically distributed with non-zero third moment, and their measure includes a continuous component. The proofs make use of Stein's method.