Three Topics in Statistics with Applications

9971791本项目包含三个主题：(1)多事件时间数据的生存分析，(2)生长曲线分析，(3)计算机化自适应测试。Topic(1)开发了满足边际比例风险要求的多事件时间参数族，并提出了边际Cox模型回归参数的半参数有效估计。它建立了间隙时间数据的非参数估计和测试程序及其大样本特性，由于（信息）权利审查，现有方法无法直接处理。本文还介绍了一类循环事件时间的半参数变换模型，并开发了易于实现且在一般假设下有效的推理过程。主题(2)处理随机增长曲线，并发展非参数检验和半参数估计程序。这里要处理的一个关键问题是如何纠正由于生长曲线不完备而引起的偏差。主题(3)发展计算机自适应测试设计和分析的统计方法。通过适当的分层，提出了新的题型选择方法，以提高题型选择的效率、题型的曝光率分布和题型的安全性。这三个主题的动机直接来自科学和教育应用。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估计。第三个话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果提供了更准确、更有效的工具。

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.