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arXiv:1206.2501 [math.PR]AbstractReferencesReviewsResources

Sharp large deviation probabilities for sums of independent bounded random variables

Xiequan Fan, Ion Grama, Quansheng Liu

Published 2012-06-12, updated 2013-08-04Version 5

We obtain some optimal inequalities on tail probabilities for sums of independent bounded random variables. Our main result completes an upper bound on tail probabilities due to Talagrand by giving a one-term asymptotic expansion for large deviations. This result can also be regarded as sharp large deviations of types of Cram\'er and Bahadur-Ranga Rao.

Comments: 19 pages, 4 figures
Categories: math.PR
Subjects: 60F10, 60E15, 60G50, 62E20
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