Statistical Theory and Methodology

统计理论与方法

• 批准号: 9504379
• 负责人: Bradley Efron
• 金额: $ 65万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-08-01 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504379&HistoricalAwards=false
• 关键词: Statistical; Theory; Methodology

Proposal: DMS 95-04379 PI: Bradley Efron Institution: Stanford University Title: Statistical Theory and Methodology' ABSTRACT: The main research areas investigated under this award include: (1) Exact methods for large, sparse contingency tables based on Markov Chain Monte Carlo techniques; (2) Improvements on the accuracy of classical normal and Edgeworth expansions, based on Stein's method; (3) The use of specially designed exponential families for density estimation and empirical Bayes situations; (4) The application of bootstrap-based techniques for confidence intervals, likelihood analysis, and bias-correction; and (5) Length and volume calculations based on Hotelling's tube formula for routine use in simultaneous testing situations. The long-term goal of this research is the development of promising theoretical ideas into methodologies of direct value to applied statisticians and their scientific clients. This form of technology transfer aims to take advantage of current developments in the range and power of new statistical methodology. The ideas here fall into the general category of "computer-intensive methods", which are methods that take advantage of modern computer power to free statistical analysis from the bounds of classical mathematical tractability. The research does not banish mathematics, but uses mathematics to produce statistical tools that can work automatically on a wide variety of problems. The computer-intensive part comes in at the level of the statistical consumer, where computation is substituted for the usual normal theory approximations and routine but difficult mathematical computations.

提案：DMS 95-04379 PI：布拉德利埃夫隆机构：斯坦福大学职位： 统计理论与方法 摘要： 该奖项的主要研究领域包括： (1)基于Markov Chain Monte Carlo技术的大型稀疏列联表的精确方法;（2）基于Stein方法，改进了经典正态展开和Edgeworth展开的准确性;（3）使用专门设计的指数族进行密度估计和经验贝叶斯情况;（4）在置信区间、似然分析和偏差校正方面应用基于Bootstrap的技术;和（5）长度和体积计算的基础上霍特林的管公式，用于日常使用的同时测试的情况。 这项研究的长期目标是将有前途的理论思想发展成为对应用统计学家及其科学客户有直接价值的方法。这种形式的技术转让旨在利用目前在新统计方法的范围和力量方面的发展。这里的思想属于“计算机密集型方法”的一般范畴，这些方法利用现代计算机的能力将统计分析从经典数学的易处理性的界限中解放出来。这项研究并没有抛弃数学，而是利用数学来产生统计工具，这些工具可以自动解决各种各样的问题。计算机密集型部分是在统计消费者的层面上出现的，在那里计算取代了通常的正常理论近似和常规但困难的数学计算。