Statistical Inverse Problems, Semiparametric Models, and Empirical Processes

建议数量。项目名称：统计逆问题、半参数模型和经验过程摘要：Jon A. Wellner将对统计逆问题、半参数模型和研究这些问题所涉及的经验过程技术进行研究。Wellner和研究生Marloes Maathuis和Leah Jager将分别研究当前状态数据算法和单调函数估计理论的竞争风险，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。本研究的第一部分将进一步研究单调函数、乘单调函数和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。研究者计划开发新的惩罚似然估计器和新的似然比检验及相关的置信区间，并引入研究最大似然估计器本身的新方法。研究人员还打算完善和改进现有的计算算法，以便对各种估计器进行额外的蒙特卡罗研究，用于似然比统计和轮廓似然，用于新的极限分布的分布理论，以及用于点过程的新分布理论。研究人员将研究新的计算算法，并对几个反问题的各种竞争算法进行比较。将发展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逆问题的统计问题。应用包括面板计数数据的回归模型，包括竞争风险模型在内的几种双变量区间剔除数据，多变量生存数据的回归模型，以及用于艾滋病毒/艾滋病研究的非参数和半参数最大似然估计的研究，以及两阶段数据依赖设计。Wellner还计划与前博士生张颖（现就职于爱荷华大学生物统计学专业）进一步研究面板计数数据的半参数模型，并与前博士生刘浩（现就职于加州大学戴维斯分校生物统计学专业）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).