Statistical Inverse Problems and Point Process Methods in Combinatorics

摘要：Jon Wellner Proposal number：DMS-0203320这项建议涉及组合学中的统计反问题和点过程方法的研究。该提案的第一部分将涉及关于似然比统计量和轮廓概率的非标准渐近性的工作，新极限分布的分布理论，以及点过程的新分布理论。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。研究的第二部分将涉及点过程方法在组合问题中的应用，包括随机排列中最长递增序列的研究以及与随机Young表有关的相关问题。

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.