On the Bennett-Hoeffding inequality
نویسنده
چکیده
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. AMS 2000 subject classifications: Primary 60E15, 60G50; secondary 60E07, 60E10, 60G42, 60G48, 60G51.
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