Mathematical Sciences: Statistics and Probability Theory of Extremes and Stable Processes

数学科学：极值和稳定过程的统计和概率论

• 批准号: 9107507
• 负责人: Tailen Hsing
• 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: 1991-08-15 至 1993-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107507&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistics; Probability; Theory

This research addresses a wide variety of interrelated problems concerning extremes, sums of dependent variables and stable processes. Many of these mathematical problems have important practical applications. The research focusses on the estimation of the distributions of extremes and uses as its principal tool the weak convergence of a point process which records the extremes. The research in statistical inference for extreme values includes investigation of properties of the extremal index and estimation of marginal tail distributions for weakly dependent variables; the research on asymptotic theory for sums of dependent variables seeks to define large classes of processes for which convergence can be established; and problems in inference for stable processes considers harmonizable stable processes and the moving average stable process.

这项研究解决了关于极值、因变量和和稳定过程的各种相互关联的问题。这些数学问题中的许多都有重要的实际应用。该研究集中于极值分布的估计，并使用记录极值的点过程的弱收敛作为其主要工具。极值统计推断的研究包括极值指数的性质和弱相依变量的边际尾部分布的估计；因变量和的渐近理论的研究旨在定义可以建立收敛的大类过程；稳定过程的推断问题考虑可协调稳定过程和移动平均稳定过程。