Mathematical Sciences: Statistical Inference for General Models

该奖项的研究工作集中在三个领域：非参数和半参数估计、平稳点过程和二十世纪统计史。非参数模型中泛函估计的具体目标包括筛估计的收敛率的研究，最优或近最优估计的构造，以及降低协变量空间维数的方法的检查。平稳点过程的研究将检验这些推理方法，也用于平稳随机集和随机场面积平均值的预测。这项研究的一个方面涉及基于物理科学复杂数据的精确估计方法的发展。这些新方法应该减少正确进行统计分析所需的假设。这项研究还将调查即使是那些必要的假设中出现轻微错误的影响。这个项目的第二个方面集中于广泛地区收集的数据的分析技术，例如大气臭氧的测量。这项工作的目标是发展统计分析方法，可用于评估不同测量之间的关系，并检查潜在的因果机制。该项目的第三个方面是对数学理论的概念结构与其科学和政策应用领域之间关系的历史研究。

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.