Mathematical Sciences: Probabilistic Limit Theorems and Applications

数学科学：概率极限定理及其应用

• 批准号: 9300725
• 负责人: Evarist Gine
• 金额: $ 9万
• 依托单位: University of Connecticut
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9300725&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Probabilistic; Limit; Theorems

The investigator will conduct research on empirical processes, U-processes, their bootstrap and some of their applications in statistics. The limit theory for degenerate U- processes has not yet reached a satisfactory stage, and the bootstrap of U-processes, degenerate or not, is far from being resolved. The applications include asymptotic theory as well as uniqueness and robustness properties of the empirical simplicial median. Open questions for U-statistics, such as almost sure convergence to zero of sums of normalized products of random variables will also be considered. Modern empirical process theory, developed during the last twenty years and not yet totally completed, not only sheds light on one of the basic questions in Statistics (namely, how well do sample properties approach population properties) but has been providing a high road to the study of important problems in asymptotic statistics. U--processes, a non-linear generalization of empirical processes, should play a similar, although more restricted, role. We propose to continue work on empirical and U--processes and their bootstraps, and to investigate some applications, such as to multidimensional robust location parameters.

研究人员将对经验过程，U过程，引导程序及其在统计数据中的某些应用进行研究。 退化U过程的极限理论尚未达到令人满意的阶段，而U退化的U过程的引导尚未得到解决。 这些应用包括经验简单中位数的渐近理论以及独特性和鲁棒性。 还将考虑开放问题的U统计数据，例如，还将考虑几乎确定肯定汇给随机变量的归一化产物总和的收敛。 现代经验过程理论，在过去的二十年中开发，尚未完全完成，不仅阐明了统计中的一个基本问题之一（即样本属性如何接近人口属性），而且还为通往该统计的属性提供了高度的道路研究渐近统计中重要问题。 u-流程是对经验过程的非线性概括，应扮演类似的角色，尽管更受限制。我们建议继续从事经验和U-过程及其引导程序，并研究某些应用，例如多维鲁棒位置参数。