ABSTRACT
ACT Probability irlequalities with exponential bourltls are very central both in proM)ility imd statistics. In particuhr, such ir~cqualitics can be used in statistic;tl (especially ~rorrpaix~lctric) iufciw~cc to provide rii t t ,~~ of collvergence for mrious cstima1,cs. In this papcr, rnaxirnal ir~equa.lities and probai~ility ir~cqualities with cxporlcr~tial 1)uuntls arc prcscntcd for mrious statistics irlclutling suns of i.i.d. rantlorn vi1l.iahles, slmls of independent but not rleccssarily it1erltic;itlly tlistri'uut,ed random variables, and U-statistics. These inequalities gcrlcrnlize itr~cl extxr~ct results of Hoeff'ding (1963), Turner, Young: a,nd Searnan (1992), Christofitles (1994) and Qiying (1996).
