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Berry–Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances

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Abstract

For sums of independent random variables \(S_n = X_1 + \cdots + X_n\), Berry–Esseen-type bounds are derived for the power transport distances \(W_p\) in terms of Lyapunov coefficients \(L_{p+2}\). In the case of identically distributed summands, the rates of convergence are refined under Cramér’s condition.

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Acknowledgements

The author would like to thank Emmanuel Rio for pointing to the preprint by T. Bonis, and the referees for valuable comments and additional references.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, MN, 55455, USA

    Sergey G. Bobkov

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  1. Sergey G. Bobkov
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Correspondence to Sergey G. Bobkov.

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Partially supported by the Alexander von Humboldt Foundation and NSF Grant DMS-1612961.

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Bobkov, S.G. Berry–Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances. Probab. Theory Relat. Fields 170, 229–262 (2018). https://doi.org/10.1007/s00440-017-0756-2

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