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

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