Mathematical Sciences: Presidential Yound Investigator Award

该研究项目是在一般领域的 数理统计与几何 概率，密度估计，渐近方法和 近似推理、决策理论和非参数 倾斜法 调查涉及可行的计算机- 数据分析的密集技术。一个总的主题的 研究是通用目的的理论发展 广泛适用于统计问题的方法。 这项统计研究解决了以下问题： 构造未知参数的置信区间 统计模型 “自动”的方法正在被 开发来处理这样的问题，由埃夫隆的工作， Bootstrap置信区间。 基于数学定理 和仿真研究，自动化的方法一般比较多， 比埃夫隆的工作准确，更容易实现， 实践

This research project is in the general area of mathematical statistics and concerns topics in geometric probability, density estimation, asymptotic methods and approximate inference, decision theory, and non-parametric tilting methods. The investigation involves viable computer- intensive techniques for data analysis. A general theme of the research is the theoretical development of general purpose methods that are widely applicable to problems in statistics. This statistical research addresses problems of constructing confidence intervals for unknown parameters in statistical models. 'Automatic' percentiles methods are being developed to handle such problems, motivated by Efron's work on bootstrap confidence intervals. Based on mathematical theorems and simulation studies, the automatic methods are generally more accurate than Efron's work and are easier to implement in practice.