Mathematical Sciences: Semiparametric Models and Empirical Processes

数学科学：半参数模型和经验过程

• 批准号: 8723011
• 负责人: Jon Wellner
• 金额: $ 13.21万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8723011&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Semiparametric; Models; Empirical

This project contains two major research themes: semiparametric models and empirical processes. Specific topics include: (1) information bounds for semiparametric models; (2) efficiency calculations for estimation problems involving althernating projection (ACE and MAP) methods; (3) construction of efficient estimates in semiparametric models including transformation models, constrained models involving infinitely many constraints, and semiparametric regression models; (4) uniformity in P of the convergence of empirical processes; (5) asympotic optimality of empirical measures; (6) preservation of the Donsker class property of a collection of functions F under projection onto a subspace in L2; (7) symmetric and quadratic statistics based on empirical measures. Research to be performed under this project is in the area of statistics.

该项目包含两个主要研究主题：半参数模型和经验过程。 具体主题包括：（1）半参数模型的信息界限； (2)涉及交替投影（ACE和MAP）方法的估计问题的效率计算； (3) 半参数模型的有效估计的构建，包括变换模型、涉及无限多个约束的约束模型和半参数回归模型； (4) 经验过程收敛的 P 的一致性； (5) 经验测度的渐近最优性； (6) 在投影到 L2 子空间上的函数集合 F 的 Donsker 类属性的保存； (7) 基于经验测量的对称和二次统计。 该项目将进行的研究属于统计学领域。