A Non-Uniform Bound of the Remainder Term in the Central Limit Theorem for Bernoulli Random Variables

S. V. Nagaev; V. I. Chebotarev; A. Ya. Zolotukhin

doi:10.1007/s10958-016-2759-4

A Non-Uniform Bound of the Remainder Term in the Central Limit Theorem for Bernoulli Random Variables

作者: Nagaev S.V.¹, Chebotarev V.I.², Zolotukhin A.Y.³
隶属关系:
1. Sobolev Institute of Mathematics SB RAN
2. Computing Center, Far Eastern Branch of RAS
3. Tula State University
期: 卷 214, 编号 1 (2016)
页面: 83-100
栏目: Article
URL: https://bakhtiniada.ru/1072-3374/article/view/237326
DOI: https://doi.org/10.1007/s10958-016-2759-4
ID: 237326

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详细

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.