论文标题
关于依赖随机变量的Stein变换与浓度不平等之间的联系
On the links between Stein transforms and concentration inequalities for dependent random variables
论文作者
论文摘要
在本文中，我们探讨了由Stein的方法和集中不平等得出的转换之间的一些联系。特别是，我们表明，随机变量的零偏置变换的随机支配相当于高斯下浓度。为此，考虑了新的随机顺序。第二次，我们研究了略微依赖的轻尾随机变量的函数案例。我们能够恢复著名的McDiarmid类型的浓度不平等，以恢复具有界限差异特性的功能。此外，当我们授权随机变量之间的光依赖性时，我们获得了新的浓度界限。最后，我们为Stein的另一种类型的变换给出了类似的结果，即所谓的尺寸偏差转换。
In this paper, we explore some links between transforms derived by Stein's method and concentration inequalities. In particular, we show that the stochastic domination of the zero bias transform of a random variable is equivalent to sub-Gaussian concentration. For this purpose a new stochastic order is considered. In a second time, we study the case of functions of slightly dependent light-tailed random variables. We are able to recover the famous McDiarmid type of concentration inequality for functions with the bounded difference property. Additionally, we obtain new concentration bounds when we authorize a light dependence between the random variables. Finally, we give a analogous result for another type of Stein's transform, the so-called size bias transform.
