Mathematical Sciences: Probability, Statistics and Functional Analysis

这项研究探讨了概率限制类 设置和功能。 经验措施可以适用于集或 函数来定义经验过程。 较早的结果 经验过程理论认为， 高斯分布对于某些类别的 设置和功能。 这项研究试图找到更大的类 统计泛函是可微的集合， 因此，可以用具有这种收敛性的过程来近似 财产，加上一个较低的秩序。

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.