Mathematical Sciences: Semiparametric Models and Empirical Processes

本研究包含两个主要的研究主题， 统计学和概率的交叉。 传统统计 依赖于参数模型的方法受到 限制参数的一个子集的欧几里德空间，而 非参数模型开始崩溃时，数据是高- 由于缺乏结构或者限制而变得多维度。 这 研究将调查半参数模型， 通过定义一类具有和正切的模型， 空间. 在这堂课上，关于效率的统计问题， 假设检验、估计和各种应用 删失或截短数据。 概率研究将集中在Donsker类， 函数及其性质，Donsker函数的应用 检验构造中椭球类的性质 基于经验的措施，以及 自举经验过程

This research contains two major research themes, both overlapping statistics and probability. Traditional statistical methods relying on parametric models are limited by the restriction of parameters to a subset of Euclidean space, while nonparametric models begin to break down when the data is high- dimensional because of a lack of structure or restriction. This research will investigate semiparametric models which lie between the two extremes by defining a class of models with sum tangent spaces. For this class, statistical questions about efficiency, hypothesis testing, estimation and applications to various kinds of censored or truncated data will be addressed. Probability research will focus on Donsker classes of functions and their properties, the application of the Donsker property for ellipsoidal classes in the construction of tests based on empirical measures, and the implications of bootstrapping empirical processes.