Mathematical Sciences: Asymptotic Problems in Statistics and Econometrics

点击翻译按钮获取中文摘要

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.