Mathematical Sciences: Asymptotic Problems in Statistics and Econometrics

在传统的假设下，估计收敛于根n率，并有渐近正态分布时，适当的标准化。该项目将研究这样的渐近失败的问题，或者传统的基于平滑度的分析方法无法处理特定问题的不寻常特征的问题。工作已经开始的例子，失败是由于一个附近缺乏可识别性，或参数空间的边界的影响，或无限维滋扰参数的影响。混合问题，其中所有这些困难自然出现，将激励的例子，对新方法进行测试。 该项目将集中在统计学和计量经济学中标准方法失效的渐近问题。PI长期以来一直参与经验过程理论领域的概率工具的开发-这是一个跨越统计学，计量经济学和计算机科学领域的领域。该项目的主要目的是调整这些工具，并发明新的方法，以应用于目前棘手的渐近问题。

Under traditional assumptions, estimators converge at root n rates and have asymptotic normal distributions when suitably standardized. The project will study problems where such asymptotics fail, or where the traditional smoothness-based methods of analysis are unable to handle unusual features of particular problems. Work has already begun on examples where the failure is due to a near lack of identifiability, or to the effects of boundaries of parameter spaces, or to the effects of infinite dimensional nuisance parameters. Mixture problems, in which all these difficulties arise naturally, will be the motivating examples against which the new methods will be tested. The project will concentrate on asymptotic problems in statistics and econometrics where the standard methods fail. The PI has long been involved in the development of probability tools in the area known as empirical process theory--an area that cuts across the fields of statistics, econometrics, and computer science. The main aim of the project is to adapt those tools, and invent new methods, to apply to currently intractable asymptotic problems.