Statistical Inverse Problems and Point Process Methods in Combinatorics

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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.