Mathematical Sciences: Bootstrap Asymptotics, Stochastic Differential Equations and Optimal Control, and Non- parametric Estimation for Diffusion Processes

数学科学：自举渐进、随机微分方程和最优控制、扩散过程的非参数估计

• 批准号: 8803639
• 负责人: Krishna Athreya
• 金额: $ 5.79万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803639&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Bootstrap; Asymptotics; Stochastic

The principal investigator will continue his study of the probabilistic properties of the resampled sample in the bootstrap methods. The investigation will extend to bootstraping stochastic processes such as Brownian motion. The effects of changing the resampling size will be explored. Resampling from a trimmed empirical rather than the original empirical distribution will be shown to be better. Limit theorems for bootstraping of the U statistics will be found. The probabilistic study of the bootstraping phenomena leads to not only interesting theorems in probability but better bootstraping methods and the validity for the existing methods.

首席研究员将继续研究bootstrap方法中重采样样本的概率特性。研究将扩展到自举随机过程，如布朗运动。我们将探讨改变重采样大小的影响。从修剪后的经验分布重新采样比从原始经验分布重新采样效果更好。将发现U统计量自举的极限定理。对自举现象进行概率研究，不仅可以得到一些有趣的概率论定理，而且可以得到更好的自举方法和现有方法的有效性。