Mathematical Sciences: Semiparametric Models and Empirical Processes

本项目包含两个主要研究主题：半参数模型和经验过程。具体内容包括：(1)半参数模型的信息边界；(2)交替投影法（ACE和MAP）估算问题的效率计算；(3)半参数模型（包括变换模型、包含无穷多约束的约束模型和半参数回归模型）有效估计的构造；(4)经验过程收敛性在P中的一致性；(5)经验测度的渐近最优性；(6) L2子空间上投影下函数集合F的Donsker类性质的保持；(7)基于经验测度的对称统计和二次统计。在这个项目下进行的研究是在统计领域。

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.