Three Topics in Statistics with Applications

统计与应用的三个主题

• 批准号: 9971791
• 负责人: Zhiliang Ying
• 金额: $ 10.82万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971791&HistoricalAwards=false
• 关键词: Three; Topics; Statistics; Applications

9971791 This project contains three topics: (1) survival analysis with multiple event-time data, (2) growth curve analysis and, (3) computerized adaptive testing. Topic (1) develops new parametric families for multiple event times that satisfy marginal proportional hazards requirement and proposes semiparametrically efficient estimator for regression parameter in the marginal Cox model. It establishes nonparametric estimation and testing procedures and their large sample properties for gap-time data, which cannot be handled directly by existing methods due to (informative) right censorship. It also introduces a class of semiparametric transformation models for recurrent event times and develops inference procedures that are easy to implement and valid under general assumptions. Topic (2) deals with random growth curves and develops nonparametric testing and semiparametric estimation procedures. A crucial issue being handled there is how to correct bias cause by incompleteness of the growth curves. Topic (3) develops statistical methods in design and analysis of computerized adaptive tests. It proposes novel approaches to item selection through suitable stratification to improve efficiency, item exposure rate distribution and test security.The three topics are motivated directly from scientific and educational applications. The first two topics are applicable to many biomedical studies including modeling of disease development, testing superiority of a new treatment and estimation of treatment efficacy. The third topic originates from the recent emergence of computerizing standardized tests, which include such widely available tests as GRE and GMAT. The new statistical methods provide more accurate and efficient tools for measuring educational achievements.

9971791本项目包括三个主题：(1)多事件-时间数据的生存分析，(2)生长曲线分析，(3)计算机化适应性测试。主题(1)发展了满足边际比例风险要求的多事件时间的新参数族，并提出了边际Cox模型中回归参数的半参数有效估计量。它为间隙时间数据建立了非参数估计和检验程序及其大样本性质，由于(信息权)审查，现有方法不能直接处理这些程序。文中还介绍了一类重现事件次数的半参数变换模型，并给出了在一般假设下易于实现和有效的推理过程。主题(2)处理随机增长曲线，并开发非参数检验和半参数估计程序。那里正在处理的一个关键问题是如何纠正增长曲线不完整造成的偏差。主题(3)开发设计和分析计算机化适应性测试的统计方法。它提出了通过适当的分层来选择试题的新方法，以提高效率、试题曝光率分布和考试安全性。这三个主题直接源于科学和教育应用。前两个主题适用于许多生物医学研究，包括疾病发展的建模、测试新治疗方法的优越性和治疗效果的评估。第三个主题源于最近出现的计算机化标准化考试，其中包括GRE和GMAT等广泛使用的考试。新的统计方法为衡量教育成就提供了更准确、更有效的工具。