On the Bennett-Hoeffding inequality
Document Type
Article
Publication Date
2-1-2014
Abstract
The well-known Bennett-Hoeffding bound for sums of independent random variables is refined, by taking into account positive-part third moments, and at that significantly improved by using, instead of the class of all increasing exponential functions, a much larger class of generalized moment functions. The resulting bounds have certain optimality properties. The results can be extended in a standard manner to (the maximal functions of) (super)martingales. The proof of the main result relies on an apparently new method that may be referred to as infinitesimal spin-off. Parts of the proof also use the method of certificates of positivity in real algebraic geometry. © Association des Publications de l'Institut Henri Poincaré, 2014.
Publication Title
Annales de l'institut Henri Poincare (B) Probability and Statistics
Recommended Citation
Pinelis, I.
(2014).
On the Bennett-Hoeffding inequality.
Annales de l'institut Henri Poincare (B) Probability and Statistics,
50(1), 15-27.
http://doi.org/10.1214/12-AIHP495
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/13129
