A remark on Bernstein, Prokhorov, Bennett, Hoeffding and Talagrand inequalities, Lithuanian Math, Journal, vol.42, issue.3, pp.262-269, 2002. ,
On Hoeffding's inequalities Annals of Probability, pp.1650-1673, 2004. ,
Optimal Hoeffding-like inequalities under a symmetry assumption, Statistics, vol.31, issue.2, pp.159-164, 2006. ,
DOI : 10.1023/A:1020269808826
A Probability Inequality for Linear Combinations of Bounded Random Variables, The Annals of Statistics, vol.2, issue.3, pp.609-613, 1974. ,
DOI : 10.1214/aos/1176342725
Sharp large deviation results for sums of independent random variables, Science China Mathematics, vol.157, issue.9, pp.1939-1958, 2015. ,
DOI : 10.1007/s00440-012-0455-y
URL : https://hal.archives-ouvertes.fr/hal-01187587
An introduction to probability theory and its applications, 1957. ,
An Improved Hoeffding's Inequality of Closed Form Using Refinemets of the Arithmetic Mean-Geometric Mean Inequality, Communications in Statistics-Theory and Methods, 2013. ,
A refinement of Hoeffding's inequality, Journal of Statistical Computation and Simulation, vol.51, issue.5, pp.977-983, 2013. ,
DOI : 10.1109/TIT.2005.846407
Some refinements of large deviation tail probabilities ,
Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963. ,
DOI : 10.1007/BF02883985
A Note on Hoeffding's Inequality, Journal of the American Statistical Association, vol.38, issue.327, pp.907-912, 1969. ,
DOI : 10.1214/aoms/1177698953
On the method of bounded differences, Soc. Lecture Note Ser, vol.141, pp.148-188, 1989. ,
DOI : 10.1017/CBO9781107359949.008
Extremal properties of sums of Bernoulli random variables, Statistics & Probability Letters, vol.62, issue.4, pp.345-354, 2003. ,
DOI : 10.1016/S0167-7152(03)00037-3
Probability inequalities for sums of independent random variables, Theory of Probab, Appl, vol.16, issue.4, pp.643-660, 1971. ,
Interpolation and approximation by polynomials, 2003. ,
DOI : 10.1007/b97417
Exact inequalities for sums of asymmetric random variables, with applications, Probab. Theory Relat, pp.605-635, 2007. ,
DOI : 10.1007/s00440-007-0055-4
URL : http://arxiv.org/pdf/math/0602556
On inequalities for sums of bounded random variables, Journal of Mathematical Inequalities, vol.2, issue.1, pp.1-7, 2008. ,
DOI : 10.7153/jmi-02-01
URL : http://arxiv.org/pdf/math/0603030v1.pdf
On the Bennett-Hoeffding inequality, Ann. Inst. Henri Poincaré Probab, Stat, vol.50, issue.1, pp.15-27, 2014. ,
DOI : 10.1214/12-aihp495
URL : http://doi.org/10.1214/12-aihp495
Chernoff???Hoeffding Bounds for Applications with Limited Independence, SIAM Journal on Discrete Mathematics, vol.8, issue.2, pp.223-250, 1995. ,
DOI : 10.1137/S089548019223872X
URL : http://ecommons.cornell.edu/bitstream/1813/6137/1/92-1305.pdf
, , 2007.
Towards a usable theory of Chernoff-Hoeffding bounds for heterogeneous and partially dependent random variables, 1992. ,
The missing factor in Hoeffding's inequalities, Ann. Inst. Henri Poincaré Probab, Stat, vol.31, pp.689-702, 1995. ,
Two refinements of the Chernoff bound for the sum of nonidentical Bernoulli random variables, Statistics & Probability Letters, vol.78, issue.12, pp.1557-1559, 2008. ,
DOI : 10.1016/j.spl.2008.01.048
A refined Hoeffding???s upper tail probability bound for sum of independent random variables, Statistics & Probability Letters, vol.131, pp.87-92, 2017. ,
DOI : 10.1016/j.spl.2017.08.012
, Czech Academy of Sciences, ? Zitná, vol.25, issue.67
, E-mail address: pelekis.chr@gmail.com INRIA Lille, 40 avenue Halley 59650 Villeneuve d'Ascq, France E-mail address: Jan.Ramon@inria.fr ETH Zurich, Distributed Computing Group