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再利用过程相关的概率问题，称为自举过程。调查员已经证明了这一领域的一些结果。现在，他建议将结果推广到方差为无穷大的情况。它还将调查当经验累积分布函数的平滑和修剪版本用于重采样时平均值的自举分布的行为。对于第二部分的研究，我们研究了临界简单分支过程。当分支过程中的方差是无穷大时，研究者将发现直到第n代的最大值的平均值的极限行为。这位研究人员一直是几乎再生过程这一概念的创始人，他将继续进行这方面的研究。