Statistical Inverse Problems and Point Process Methods in Combinatorics

组合数学中的统计反问题和点过程方法

• 批准号: 0203320
• 负责人: Jon Wellner
• 金额: $ 22.5万
• 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: 2002
• 资助国家: 美国
• 起止时间: 2002-07-15 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0203320&HistoricalAwards=false
• 关键词: Statistical; Inverse; Problems; Point; Process

AbstractPI: Jon WellnerProposal Number: DMS-0203320This proposal deals with research on statistical inverse problems and point process methods in combinatorics. The first part of the proposal will involve work on non-standard asymptotics for likelihood ratio statistics and profile likelihoods, distribution theory for new limiting distributions, and new distribution theory for point processes. New computational algorithms will be investigated and comparisons of various competing algorithms for several inverse problems will be studied. 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, regression models for multivariate survival data, and studies of non- and semi-parametric maximum likelihood estimators used in AIDS research, two-phase data dependent designs, and animal carcinogenesis experiments.The second part of the research will involve applications of point process methods to combinatorial problems, including study of the longest increasing sequence in a random permutation and related problems concerning random Young tableaux.

摘要PI：Jon Wellner提案编号：DMS-0203320本提案涉及组合学中统计逆问题和点过程方法的研究。该提案的第一部分将涉及似然比统计和轮廓似然的非标准渐近性，新的极限分布的分布理论，以及点过程的新分布理论。新的计算算法将被调查和各种竞争算法的几个反问题的比较将被研究。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。应用包括面板计数数据的回归模型，几种双变量区间删失数据，多变量生存数据的回归模型，以及艾滋病研究中使用的非参数和半参数最大似然估计的研究，两阶段数据相关设计，和动物致癌实验。包括随机排列中最长递增序列的研究以及随机Young表的相关问题。