Email this article On Large Deviations for Sums of i.i.d. Bernoulli Random Variables
- Authors: Nagaev S.V.1, Chebotarev V.I.2,3
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Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch of RAS
- Computing Center, Far Eastern Branch of RAS
- Far Eastern State Transport University
- Issue: Vol 234, No 6 (2018)
- Pages: 816-828
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242015
- DOI: https://doi.org/10.1007/s10958-018-4049-9
- ID: 242015
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Abstract
Tail probabilities are studied for the binomial distribution. The Hoeffding inequality is sharpened in this particular case through estimating an integral factor in the Esscher transform, which is omitted in Hoeffding’s proof. This approach was already used by Talagrand (1995) in the general case. However, our results are much more precise. In particular, all involved constants are given in the explicit form.
About the authors
S. V. Nagaev
Sobolev Institute of Mathematics, Siberian Branch of RAS
Author for correspondence.
Email: nagaev@math.nsc.ru
Russian Federation, Novosibirsk
V. I. Chebotarev
Computing Center, Far Eastern Branch of RAS; Far Eastern State Transport University
Email: nagaev@math.nsc.ru
Russian Federation, Vladivostok; Khabarovsk
