论文标题
独立随机变量与功率类型的独立随机变量线性组合的无矩偏差不平等
Moment free deviation inequalities for linear combinations of independent random variables with power-type tails
论文作者
论文摘要
在所有随机变量都满足相同的功率型尾巴上的假设，我们提出了非负随机变量非阴性线性组合的分位数的数量估计顺序估计，以及对独立随机变量的一般线性组合的偏差不等式。形式$ t^{ - q} $，$ t^{ - q/2} $或$ t^{ - q/2}（\ ln t）^{q/2} $，对于$ q> 2 $。第三种类型适用于非线性设置。在我们考虑的情况下，这些结果改善了Nagaev的经典估计。
We present order of magnitude estimates for the quantiles of non-negative linear combinations of non-negative random variables, as well as deviation inequalities for general linear combinations of independent random variables, under the assumption that all random variables satisfy the same power-type tail bound on $\mathbb{P}\{\left\vert X_i\right\vert>t\}$ of the form $t^{-q}$, $t^{-q/2}$ or $t^{-q/2}(\ln t)^{q/2}$, for $q>2$. The third type is applicable in the nonlinear setting. In the situations we consider, these results improve on classical estimates of Nagaev.
