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

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arxiv 2305.14248 v4 pith:3QBQAIE6 submitted 2023-05-23 math.PR

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keywords centralconvergencelimitmultivariatenon-zeroratetheoremwasserstein
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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.

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