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

Thomas Bonis

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arXiv · 2305.14248

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

Thomas Bonis

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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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Thomas Bonis. 2023-05-23. Improved rates of convergence for the multivariate Central Limit Theorem in Wasserstein distance. https://arxiv.org/abs/2305.14248

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