Mathematical Sciences: Bootstrap Asymptotics in Statistics and Stochastic Processes and Limit Therorems for Branching and Almost Regenerative Processes

数学科学：统计和随机过程中的自举渐近以及分支和几乎再生过程的极限定理

• 批准号: 8706319
• 负责人: Krishna Athreya
• 金额: $ 2.53万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1988-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8706319&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Bootstrap; Asymptotics; Statistics

This research will study the probability questions related to the sample re-use procedure called the bootstraping. The investigator has already proved a number of results in this area. Now he proposes to extend the results to the cases when the variance is infinite. It will also investigate the behavior of the bootstrap distribution of the mean when a smoothed and trimmed version of the empirical cummulative distribution function is used for resampling. For the second part of the research, critical simple branching processes are studied. The investigator will find the limiting behavior of the mean of the maximum up to the n-th generation when the variance in the branching process is infinite. The investigator, who has been the originator of the idea of almost regenerative processes, will continue his study of the same.

本研究将研究与样本重用程序（称为引导程序）相关的概率问题。 研究人员已经证明了这方面的一些结果。 现在他建议将结果扩展到方差无穷大的情况。 它还将研究当经验累积分布函数的平滑和修剪版本用于重采样时均值的自举分布的行为。 对于研究的第二部分，研究了关键的简单分支过程。 当分支过程的方差无穷大时，研究者将发现直到第 n 代的最大值均值的极限行为。 这位研究人员是几乎再生过程概念的创始人，他将继续对此进行研究。