Mathematical Sciences: Quantile-Uniform Empirical Distribution Function Methods in Probability Theory

数学科学：概率论中的分位数均匀经验分布函数方法

• 批准号: 9002731
• 负责人: David Mason
• 金额: $ 4.34万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002731&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Quantile; Uniform; Empirical

The principal investigator will continue his work in probability theory in the area of empirical processes. Essential to his quantile-uniform empirical distribution function approach is the study of the large sample properties of the uniform empirical process and their relationship through the probability integral transformation to those of arbitrary real valued random variables. He will consider problems on the studies of limit results for sums of intermediate extreme values and records, functional laws of the iterated logarithm for increment processes and a notion of generalized quantiles. The principal investigator will continue his work in probability theory in the area of empirical processes. Empirical processes theory has largely been concerned with uniform analogues of the classical limit theorems for sums of independent random variables, which is the foundations of mathematical statistics. The investigator will continue to develope an approach he developed to study limit theorems for intermediate extreme values.

首席研究员将继续他在经验过程领域的概率论方面的工作。他的分位数-均匀经验分布函数方法的核心是通过对任意实值随机变量的概率积分变换，研究均匀经验过程的大样本性质及其相互关系。他将考虑中间极值和记录和的极限结果的研究问题，增量过程的迭代对数的泛函规律和广义分位数的概念。首席研究员将继续他在经验过程领域的概率论方面的工作。经验过程理论在很大程度上关注于独立随机变量和的经典极限定理的一致类似，这是数理统计的基础。研究者将继续发展他开发的方法来研究中间极值的极限定理。