Mathematical Sciences: Asymptotic Problems in Statistics and Econometrics

在传统的假设下，估计量收敛于根n率，并且在适当标准化时具有渐近正态分布。该项目将研究这样的渐近性失效的问题，或者传统的基于平滑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中，失败是由于几乎缺乏可辨识性，或由于参数空间的边界的影响，或由于无限维扰扰参数的影响。所有这些困难自然而然地出现的混合问题，将是新方法将被测试的激励例子。该项目将专注于统计学和计量经济学中的渐近问题，这些问题是标准方法无法解决的。长期以来，PI一直参与开发被称为经验过程理论的概率工具--这一领域横跨统计学、计量经济学和计算机科学。该项目的主要目标是调整这些工具，并发明新的方法，以应用于目前难以解决的渐近问题。

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.