Mathematical Sciences: Semiparametric Models and Empirical Processes

该项目包含两个主要研究主题： 半参数模型和经验过程。 具体专题 包括：（1）半参数模型的信息界;（2） 估算问题的效率计算， 交替投影（ACE和MAP）方法;（3）构造 半参数模型中的有效估计，包括 转换模型，约束模型，涉及无限 多约束和半参数回归模型;（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） 函数集合F的Donsker类性质 投影到L2中的子空间;（7）对称和二次 基于经验的统计。 在本项目下进行的研究是在该地区 的统计数据。

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.