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Sharp large deviation results for sums of independent random variables
Abstract : We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand (1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram\'{e}r (1938), Bahadur-Rao (1960) and Sakhanenko (1991). We also show that our bound can be used to improve a recent inequality of Pinelis (2014).
Cited literature [47 references]
https://hal.inria.fr/hal-01187587
Contributor : Xiequan Fan <>
Submitted on : Friday, August 28, 2015 - 1:27:03 PM
Last modification on : Saturday, May 1, 2021 - 3:50:44 AM
Long-term archiving on: : Sunday, November 29, 2015 - 10:17:13 AM
Contributor : Xiequan Fan <>
Submitted on : Friday, August 28, 2015 - 1:27:03 PM
Last modification on : Saturday, May 1, 2021 - 3:50:44 AM
Long-term archiving on: : Sunday, November 29, 2015 - 10:17:13 AM
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