Abstract In this Note, we provide exponential inequalities for suprema of empirical processes with heavy tails on the left. Our approach is based on a martingale decomposition, associated with comparison inequalities over a cone of convex functions originally introduced by Pinelis. Furthermore, the constants in our inequalities are explicit.

中文翻译：

---

左重尾的经验过程至上的指数不等式

摘要 在这篇笔记中，我们为左侧有重尾的经验过程的至上提供了指数不等式。我们的方法基于马丁格尔分解，与最初由 Pinelis 引入的凸函数锥上的比较不等式相关联。此外，我们不等式中的常数是明确的。