Statistical Inverse Problems, Semiparametric Models, and Empirical Processes

建议编号：0503822INSTUTION：华盛顿大学NSF计划：STATISTICSPRINCIPAL调查员和联合PI：Wellner，Jon APROPOSAL标题：统计反问题，半参数模型，和经验过程摘要Jon A.Wellner将对研究这些问题所涉及的统计反问题，半参数模型和经验过程技术进行研究。Wellner和研究生Marloes Maathuis和Leah Jager将分别使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一系列新的拟合优度测试来研究竞争风险。本研究的第一部分将进一步研究单调、乘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器和新的似然比检验以及相关的置信度区间，并引入研究最大似然估计量本身的新方法。研究人员还打算改进和改进现有的计算算法，以便可以对似然比统计量和轮廓似然、新的极限分布的分布理论和点过程的新的分布理论进行其他各种估计量的蒙特卡罗研究。研究人员将研究几个反问题的新计算算法和各种竞争算法的比较。将开发基本的经验过程工具和方法，并将其应用于有关半参数模型和反问题的统计问题。应用包括面板计数数据的回归模型、几种类型的双变量区间删失数据(包括竞争风险模型)、多变量生存数据的回归模型、用于HIV-AIDS研究的非参数和半参数最大似然估计量的研究，以及两阶段数据依赖设计。Wellner还计划与前博士生张颖(现供职于爱荷华大学生物统计学)一起对面板计数数据的半参数模型进行进一步研究，并与前博士生刘浩(现供职于加州大学戴维斯分校生物统计)进一步研究涉及多个计数过程的纵向数据。

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).