Sharp large deviation probabilities for sums of independent bounded random variables

摘要

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