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Sharp large deviation probabilities for sums of independent bounded random variables (1206.2501v5)
Published 12 Jun 2012 in math.PR
Abstract: 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.
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