Mathematical Sciences: Regular Variation: Analytic Approaches to Probability and Statistics

数学科学：正则变分：概率与统计的分析方法

• 批准号: 9101083
• 负责人: Daren Cline
• 金额: $ 1.92万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1993-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101083&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Regular; Variation; Analytic

The mathematical analytic concept of regular variation is fundamental for the study of sums and of extremes. This research will investigate the applications of this branch of analysis to a wider range of topics in probability and statistics, particularly to infinitely divisible distributions and Levy processes, to nonparametric function estimation, to long-range dependence of variables, and to regression problems with infinite variance and/or large deviations. Multivariate subexponentiality, a related concept, will be studied as it relates to tail-behavior of extremes and of sums of random variables.

正则变分的数学分析概念是 是研究求和和极值的基础。 本研究 我将研究这一分析分支的应用， 在概率和统计的更广泛的主题，特别是 无限可分分布和Levy过程， 非参数函数估计，对 变量，以及具有无穷方差的回归问题 和/或大偏差。 多元次指数性，a 相关的概念，将研究，因为它涉及到尾部的行为 极值和随机变量之和的概率。