Mathematical Sciences: Probability, Statistics and Functional Analysis

本研究考察了集合和函数类的概率极限。经验度量可以应用于集合或函数来定义经验过程。经验过程理论的早期结果表明，对于某些集合和函数类，分布收敛于高斯分布是一致的。本研究旨在寻找统计函数可微的更大的集合类，因此可以用具有这种收敛性质的过程加上低阶的余数来近似。

This research examines probability limits over classes of sets and functions. Empirical measures can be applied to sets or to functions to define empirical processes. Earlier results in empirical process theory established that convergence in distribution to a Gaussian holds uniformly for certain classes of sets and functions. This research seeks to find larger classes of sets for which statistical functionals are differentiable and therefore can be approximated by a process with this convergence property, plus a remainder of lower order.