Mathematical Sciences: Estimation in Semiparametric Models and Empirical Processes

数学科学：半参数模型和经验过程中的估计

• 批准号: 9532039
• 负责人: Jon Wellner
• 金额: $ 13.82万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2002-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9532039&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Estimation; Semiparametric; Models

DMS 95-32039: Wellner This research involves the study of empirical processes, bootstrap methods in statistics, semiparametric models, and inverse problems and nonstandard asymptotics. The research will involve limit theory for infinite - dimensional M - estimates and related bootstrap methods, preservation theorems for uniform Donsker classes of functions, uniform in P bootstrap limit theorems, estimation of monotone and convex functions, convergence of iterative convex minorant algorithms, and the behavior of global functionals in models with interval censoring. %%% For the analysis of failure time data which are subject to right censoring and/or left truncation, many methods are now available. However, in many biomedical studies, including those arising from HIV/AIDS studies, failure times are censored or truncated in more complicated ways. One such complication is ``interval censoring'', in which one knows that the event of interest occurs within a random time interval, but not the exact timing: for example, HIV positivity or the drop of the CD4 count below a certain threshold may only be determined to be between two clinical visits, but not the exact time may remain unknown. This research will involve developing new statistical method for data arising from these and other more complicated censoring mechanisms ranging from animal carcinogenesis experiments to data in sociology and econometrics modelling. A detailed study and evaluation of the properties of methods recently proposed by other statisticians will be completed. ***

DMS 95 - 32039：Wellner 本研究涉及经验过程的研究，统计学中的bootstrap方法，半参数模型， 反问题和非标准渐近性。 这项研究将 涉及无限维M-估计极限理论， 相关的bootstrap方法，一致Donsker保持定理 类的功能，一致的P自助极限定理， 单调函数和凸函数的估计，迭代收敛性 凸次优算法，以及全局泛函在 区间删失模型 %%%用于分析故障时间数据， 截尾和/或左截断，现在有许多方法可用。 然而，在许多生物医学研究中，包括那些由 艾滋病毒/艾滋病研究，失败时间被审查或截断， 复杂的方式。 一个这样的复杂性是“区间删失”， 其中人们知道感兴趣的事件发生在随机的 时间间隔，但不是确切的时间：例如，HIV阳性 或者CD4计数下降到某个阈值以下可能只是 确定在两次临床访视之间，但确切时间可能仍然未知。 这项研究将涉及开发新的 这些和其他更多数据统计方法 复杂的审查机制， 致癌实验的社会学数据， 计量经济学模型 详细的研究和评估 其他统计学家最近提出的方法的性质 将完成。 ***