Email this article A Non-Uniform Bound of the Remainder Term in the Central Limit Theorem for Bernoulli Random Variables
- Authors: Nagaev S.V.1, Chebotarev V.I.2, Zolotukhin A.Y.3
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Affiliations:
- Sobolev Institute of Mathematics SB RAN
- Computing Center, Far Eastern Branch of RAS
- Tula State University
- Issue: Vol 214, No 1 (2016)
- Pages: 83-100
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237326
- DOI: https://doi.org/10.1007/s10958-016-2759-4
- ID: 237326
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Abstract
A bound for the remainder in the Esseen expansion is obtained in the case of Bernoulli random variables. The bound consists of two parts, uniform and non-uniform. The uniform part depends only on n and p, and the non-uniform part depends also on x. This bound is compared with other known bounds. It is shown how this result can be applied to the problem of the absolute constant in the Berry–Esseen inequality.
About the authors
S. V. Nagaev
Sobolev Institute of Mathematics SB RAN
Author for correspondence.
Email: nagaev@math.nsc.ru
Russian Federation, Novosibirsk
V. I. Chebotarev
Computing Center, Far Eastern Branch of RAS
Email: nagaev@math.nsc.ru
Russian Federation, Khabarovsk
A. Ya. Zolotukhin
Tula State University
Email: nagaev@math.nsc.ru
Russian Federation, Tula
