Mathematical Sciences: Statistical Inference for General Models

该奖项下的研究工作包括三个领域： 非参数和半参数估计，平稳点 过程和二十世纪统计的历史。 非参数泛函估计的具体目标 模型包括对筛估计的收敛速率的研究， 最优或接近最优估计的构造，以及 检验降低协变量维数的方法 空间 平稳点过程的研究将考察 这些的推理方法，也适用于平稳随机集 以及随机场的面积平均值的预测。 这项研究的一个方面涉及发展 基于复杂数据的精确估计方法 物理科学 这些新方法将减少 进行统计分析所需的假设 正确 该研究还将调查轻度 即使是那些必要的假设也是错误的。 的第二方面 该项目侧重于数据分析技术 在广泛的领域收集，例如，测量 大气臭氧 这项工作的目标是发展 可用于评估的统计分析方法 不同测量之间的关系，并检查 潜在的因果机制。 这个项目的第三个方面是 概念关系的历史研究 数学理论的科学结构 政策应用。

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.