Abstract
We provide new bounds for the rate of convergence of the multivariate Central Limit Theorem in Wasserstein distances of order . 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.
Acknowledgments
I would like to thank the anonymous referee for their many comments which helped improve this paper. I am also grateful to Olivier Guédon for pointing out [8] to me.
Citation
Thomas Bonis. "Improved rates of convergence for the multivariate Central Limit Theorem in Wasserstein distance." Electron. J. Probab. 29 1 - 18, 2024. https://doi.org/10.1214/24-EJP1134
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