Shape Restrictions, Semiparametric Models, and Empirical Processes

形状限制、半参数模型和经验过程

• 批准号: 0804587
• 负责人: Jon Wellner
• 金额: $ 26万
• 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: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0804587&HistoricalAwards=false
• 关键词: Shape; Restrictions; Semiparametric; Models; Empirical

Jon A. Wellner will carry out research on empirical process methods and computational strategies for a variety of semiparametric and nonparametric models for shape restrictions, censored data, and missing data problems.In particular, Wellner and University of Washington graduate student Marios Pavlides will conduct research on several models involving multivariate monotone density functions and multivariate current status observation schemes, a class of models currently of interest in connection with HIV-AIDS studies. Wellner and University of Washington graduate student Arseni Seregin will conduct research on nonparametric estimation of log-concave densities and generalizations thereof in one and higher dimensions. Some of the research on empirical processes will be carried out jointly with Aad van der Vaart (Free University, Amsterdam). Some of the research on inference under shape constraints will be carried out jointly with Fadoua Balabdaoui, Marloes Maathuis, and Shuguang Song (former Ph.D. students). The work on new computational algorithms will be carried out jointly with Hanna Jankowski, a recent post-doctoral student at the University of Washington and now a faculty member at York University, Canada. These investigations will involve nonstandard asymptotics for maximum likelihood estimators, likelihood ratio statistics, and distribution theory for new nonstandard limit distributions.The research will involve development of basic empirical process tools and methods, and applications of these new tools and methods to statistical problems concerning semiparametric models, shape restricted models, and inverse problems. Applications include regression models for panel count data, bivariate interval censored data of several kinds, regression models for survival data with missing covariate data, studies of non- and semi-parametric maximum likelihood estimators used in AIDS research, new confidence bands for shape restricted inference, and both basic empirical process theory and new semiparametric estimation procedures for two-phase data dependent designs. The advances in inference methods for competing risks models are used to study causative effects of viral loading in HIV vaccine trials. The developments in bivariate censored data are applied to studies of mother-to-child transmission of HIV-AIDS. The work on two-phase data dependent designs has application to new designs with increased efficiency for clinical trials and case-cohort sampling in epidemiology. The tools of empirical process theory allow investigations of many problems of current interest in other areas of statistics involving high-dimensional data and parameter spaces. The research benefits education and human development by the training of graduate students and the inclusion of the resulting new statistical methods in statistics courses at the University of Washington and elsewhere.

乔恩·A Wellner将针对形状限制、删失数据和缺失数据问题开展各种半参数和非参数模型的经验处理方法和计算策略的研究，特别是Wellner和华盛顿大学研究生Marios Pavlides将对涉及多元单调密度函数和多元现状观测方案的几个模型进行研究，一类目前与艾滋病毒/艾滋病研究有关的模型。Wellner和华盛顿大学的研究生Arseni Seregin将在一维和高维中对对数凹密度的非参数估计及其推广进行研究。 将与Aad货车der Vaart（阿姆斯特丹自由大学）联合进行一些关于经验过程的研究。一些关于形状约束下的推理的研究将与Fadoua Balabdaoui，Marloes Maathuis和Shuguang Song（前博士）联合进行。学生）。新计算算法的研究将与Hanna Jankowski联合进行，Hanna Jankowski最近在华盛顿大学攻读博士后，现在是加拿大约克大学的教员。这些研究将涉及极大似然估计的非标准渐近性、似然比统计和新的非标准极限分布的分布理论，研究将涉及基本经验过程工具和方法的发展，以及这些新工具和方法在半参数模型、形状限制模型和逆问题的统计问题中的应用。应用包括回归模型面板计数数据，双变量区间删失数据的几种，回归模型的生存数据与缺失的协变量数据，研究非和半参数的最大似然估计用于艾滋病研究，新的置信带形状限制的推理，和基本的经验过程理论和新的半参数估计程序的两个阶段的数据依赖设计。竞争风险模型的推理方法的进展被用于研究HIV疫苗试验中病毒载量的因果效应。 双变量删失数据的发展被应用于母婴传播艾滋病毒/艾滋病的研究。 两阶段数据依赖设计的工作可应用于新设计，提高临床试验和流行病学病例队列抽样的效率。经验过程理论的工具允许调查的许多问题，目前的兴趣在其他领域的统计，涉及高维数据和参数空间。这项研究通过培训研究生和将由此产生的新统计方法纳入华盛顿大学和其他地方的统计课程，有益于教育和人类发展。