Mathematical Sciences: Statistical Inference for General Models

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Research efforts under this award lie in three areas: nonparametric and semiparametric estimation, stationary point processes and the history of twentieth century statistics. Specific goals for estimation of functionals in nonparametric models include a study of convergence rates for sieve estimators, the construction of optimal or near-optimal estimators, and an examination of ways to reduce the dimensionality of the covariate space. The study of stationary point processes will examine methods of inference for these, also for stationary random sets and for the prediction of areal averages of random fields. One facet of this research involves the development of methods of accurate estimation based on complex data from the physical sciences. These new methods should reduce the assumptions needed for the statistical analysis to proceed correctly. The research will also investigate the effect of mild errors in even those necessary assumptions. A second aspect of this project focusses on the analytic techniques for data gathered over wide areas, for example, measurements of atmospheric ozone. The goal of this work is to develop statistical analytical methods which can be used to evaluate relationships among different measurements and to examine potential causal mechanisms. The third aspect of this project is the historical study of the relationship of the conceptual structure of mathematical theories to their areas of scientific and policy applications.