On the Bennett-Hoeffding inequality

Abstract

The well-known Bennett-Hoeffding bound for sums of independent random variables is refined, by taking into account truncated third moments, and at that also improved by using, instead of the class of all increasing exponential functions, the much larger class of all generalized moment functions f such that f and f" are increasing and convex. It is shown that the resulting bounds have certain optimality properties. Comparisons with related known bounds are given. The results can be extended in a standard manner to (the maximal functions of) (super)martingales.

References in corpus (4)

• Concentration around the mean for maxima of empirical processes
• Exact inequalities for sums of asymmetric random variables, with applications
• Binomial upper bounds on generalized moments and tail probabilities of (super)martingales with differences bounded from above
• Positive-part moments via the Fourier-Laplace transform

Cited by in corpus (4)

• Polynomial bounds in the Ergodic Theorem for positive recurrent one-dimensional diffusions and integrability of hitting times
• Positive-part moments via the Fourier-Laplace transform
• Sharp large deviation results for sums of independent random variables
• An asymptotically Gaussian bound on the Rademacher tails