Statistical Inverse Problems, Semiparametric Models, and Empirical Processes

统计反问题、半参数模型和经验过程

• 批准号: 0503822
• 负责人: Jon Wellner
• 金额: --
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0503822&HistoricalAwards=false
• 关键词: Statistical; Inverse; Problems; Semiparametric; Models

PROPOSAL NUMBER.: 0503822INSTITUTION: University of WashingtonNSF PROGRAM: STATISTICSPRINCIPAL INVESTIGATOR and Co-PI: Wellner, Jon APROPOSAL TITLE: Statistical Inverse problems, Semiparametric Models, and Empirical Processes Abstract Jon A. Wellner will carry out research on statistical inverse problems, semi-parametric models, and on empirical process techniques involved in studying these problems. Wellner and graduate students Marloes Maathuis and Leah Jager will carry out research on competing risks with current status data algorithms and theory for monotone function estimation, and a new family of goodness-of-fit tests related to the Berk-Jones statistic and the associated confidence bands, respectively. The first part of this research will involve further study of nonstandard asymptotics for maximum likelihood and leastsquares estimators of monotone, multiply monotone and completely monotone functions. The investigator plans to develop new penalized likelihood estimators and new likelihood ratio tests and related confidence intervals, as well as introduce new methods of studying the maximum likelihood estimators themselves. The investigator also intends to refine and improve the existing computational algorithms to the point where additional monte-carlo studies of the various estimators can be carried out for likelihood ratio statistics and profile likelihoods, distribution theory for new limiting distributions, and new distribution theory for point processes. The investigator will investigate new computational algorithms and comparisons of various competing algorithmsfor several inverse problems. Basic empirical process tools and methods will be developed and applied to statistical problems concerning semiparametric models and inverse problems. Applications include regression models for panel count data, bivariate interval censored data of several kinds including models for competing risks, regression models for multivariate survival data, and studies of non- and semi-parametric maximum likelihood estimators used in HIV-AIDS research, and two-phase data dependent designs. Wellner also plans to conduct further research on semiparametric models for panel count data with former Ph.D. student Ying Zhang (now at the University of Iowa, Biostatistics) and further work on longitudinal data involving multiple counting processes with former Ph.D. student Hao Liu (now at the University of California at Davis, Biostatistics).

提案编号：0503822机构：华盛顿大学NSF研究员：统计学、半参数模型和经验过程：Wellner，Jon APROPOSAL标题：统计逆问题、半参数模型和经验过程 摘要Jon A.韦尔纳将开展统计逆问题，半参数模型，并在研究这些问题所涉及的经验过程技术的研究。Wellner和研究生Marloes Maathuis和Leah Jager将分别利用当前状态数据算法和单调函数估计理论以及与Berk-Jones统计量和相关置信带相关的新拟合优度检验家族对竞争风险进行研究。本研究的第一部分将进一步研究单调、多重单调和完全单调函数的极大似然估计和最小二乘估计的非标准渐近性。 研究人员计划开发新的惩罚似然估计和新的似然比检验和相关的置信区间，以及引入研究最大似然估计本身的新方法。研究人员还打算完善和改进现有的计算算法，使其达到可以对似然比统计和剖面似然、新极限分布的分布理论和点过程的新分布理论进行各种估计量的额外蒙特-卡罗研究的程度。 调查员将调查新的计算算法和几个反问题的各种竞争算法的比较。 基本的经验过程工具和方法将被开发和应用于有关半参数模型和逆问题的统计问题。 应用程序包括面板计数数据的回归模型，双变量区间删失数据的几种类型，包括模型的竞争风险，回归模型的多变量生存数据，和研究的非和半参数最大似然估计用于艾滋病毒-艾滋病的研究，和两个阶段的数据依赖设计。 Wellner还计划与前博士一起对面板计数数据的半参数模型进行进一步研究。学生Ying Zhang（现就职于爱荷华州大学生物统计学系），并与前博士生Ying Zhang（现就职于爱荷华州大学生物统计学系）一起进一步研究涉及多个计数过程的纵向数据。学生刘昊（现就职于加州大学戴维斯分校生物统计学专业）。