Mathematical Sciences: Semiparametric Models and Empirical Processes

这个项目包含两个主要的研究主题：半参数模型和经验过程。具体的主题包括：(1)半参数模型的信息界；(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(包括变换模型、包含无限多约束的约束模型和半参数回归模型)中有效估计的构造；(4)经验过程收敛在P中的一致性；(5)经验测度的渐近最优性；(6)在L2中子空间的投影下保持函数集合F的Donsker类性质；(7)基于经验测度的对称和二次统计量。在该项目下要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.