Mathematical Sciences: Asymptotic Problems in Statistics and Econometrics

在传统假设下，估计量以根n速率收敛，并且在适当标准化时具有渐近正态分布。该项目将研究这些渐近性失效的问题，或者传统的基于平滑性的分析方法无法处理特定问题的异常特征的问题。对于由于几乎缺乏可识别性，或由于参数空间边界的影响，或由于无限维讨厌参数的影响而失败的例子，工作已经开始。所有这些困难自然会出现在混合问题中，混合问题将成为测试新方法的激励例子。该项目将集中于统计和计量经济学中标准方法失效的渐近问题。PI长期以来一直参与概率工具在经验过程理论领域的发展，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适应这些工具，并发明新的方法，以适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.