US-France Cooperative Research: The Asymptotic Behavior of Increment and Tail Processes

该奖项将支持特拉华大学的David Mason博士和法国巴黎六世大学理论和应用统计实验室的Paul Deheuvells教授在统计和概率方面的合作研究。研究人员将集中于以下领域：1)增量过程，包括经验过程增量的泛函重对数律、非参数函数估计和两个样本Bahaduir-Kiefer检验统计量；以及2)尾部过程，其中包括关于分布尾部的统计推断和异常值检验。关于分布的上尾部的推断有许多重要的应用，如在保险中估计大额索赔的概率，或在工程中确定建造大坝或石油平台的合理安全高度。这两名研究人员被认为是这一数学领域的主要研究人员，拟议的项目将受益于他们互补的专业知识和以前成功的合作努力。

This award will support collaborative research in statistics and probability between Dr. David Mason, University of Delaware and Professor Paul Deheuvels, Laboratory for Theoretical and Applied Statistics, University of Paris VI, France. The investigators will focus on the following areas: 1) increment processes, which include functional laws of the iterated logarithm for the increments of the empirical process, nonparametric function estimation and two sample Bahaduir-Kiefer test statistics, and 2) tail processes, which among other problems encompass statistical inference about the tails of a distribution and testing for outliers. Inference about the upper tail of a distribution has a large number of important applications, such as in insurance to estimate the probability of a large claim or in engineering to determine a reasonable safe height to construct a dam or oil platform. The two investigators are considered leading researchers in this area of mathematics and the proposed project will benefit from their complementary expertise and previous successful collaborative efforts.