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Refinements of Berry–Esseen Inequalities in Terms of Lyapunov Coefficients

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Abstract

We discuss some variants of the Berry–Esseen inequality in terms of Lyapunov coefficients which may provide sharp rates of normal approximation.

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Acknowledgements

This work was partially supported by the NSF grant DMS-2154001 and the BSF grant 2016050. We would like to thank Iosif Pinelis for the reference to the Cox-Kemperman inequality and two referees for careful reading and valuable remarks.

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  1. School of Mathematics, University of Minnesota, 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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Communicated by Vladimir Protasov.

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Bobkov, S.G. Refinements of Berry–Esseen Inequalities in Terms of Lyapunov Coefficients. J Fourier Anal Appl 29, 72 (2023). https://doi.org/10.1007/s00041-023-10054-y

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