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Theory of Probability and Mathematical Statistics

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Estimation of the rate of convergence in the central limit theorem for a sequence of series in terms of averaged pseudomoments


Authors: M. M. Kapustei and P. V. Slyusarchuk
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 99 (2018).
Journal: Theor. Probability and Math. Statist. 99 (2019), 101-111
MSC (2010): Primary 60F05
DOI: https://doi.org/10.1090/tpms/1083
Published electronically: February 27, 2020
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Abstract | References | Similar Articles | Additional Information

Abstract: A generalization of Zolotarev's estimates is proved for a sequence of series of random variables. The estimates are expressed in terms of averaged pseudomoments.


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Additional Information

M. M. Kapustei
Affiliation: Department of Probability Theory and Mathematical Analysis, Faculty for Mathematics, Uzhgorod National University, Universytets’ka Street, 14, Uzhgorod, 88020 Ukraine
Email: michaelkapustey@gmail.com

P. V. Slyusarchuk
Affiliation: Department of Probability Theory and Mathematical Analysis, Faculty for Mathematics, Uzhgorod National University, Universytets’ka Street, 14, Uzhgorod, 88020 Ukraine
Email: petro_slyusarchuk@ukr.net

DOI: https://doi.org/10.1090/tpms/1083
Keywords: Convergence, central limit theorem, pseudomoments, sequence of series, nonidentically distributed random variables
Received by editor(s): June 25, 2018
Published electronically: February 27, 2020
Article copyright: © Copyright 2020 American Mathematical Society