论文标题
使用更高的矩信息的集中不平等
Concentration inequalities using higher moments information
论文作者
论文摘要
在本文中，我们使用有关随机变量较高矩的信息概括并改善了一些基本浓度不平等。特别是，我们改善了经典的Hoeffding和Bennett的不平等现象，对于每个正整数$ p $的随机变量的第一个$ p $矩都有一些信息。重要的是，我们广义的Hoeffding的不平等比Hoeffding的不平等程度更紧密，并且在每个正整数$ p $的简单闭合表达中给出。因此，广义的Hoeffding的不平等在应用中易于使用。为了证明我们的结果，我们在随机变量的第一个$ p $ iments的随机变量的生成函数上得出了新颖的上限，并表明这些界限满足了适当的凸度属性。
In this paper, we generalize and improve some fundamental concentration inequalities using information on the random variables' higher moments. In particular, we improve the classical Hoeffding's and Bennett's inequalities for the case where there is some information on the random variables' first $p$ moments for every positive integer $p$. Importantly, our generalized Hoeffding's inequality is tighter than Hoeffding's inequality and is given in a simple closed-form expression for every positive integer $p$. Hence, the generalized Hoeffding's inequality is easy to use in applications. To prove our results, we derive novel upper bounds on the moment-generating function of a random variable that depend on the random variable's first $p$ moments and show that these bounds satisfy appropriate convexity properties.
