文章基本信息

标题：Jackknife, small bandwidth and high-dimensional asymptotics
本地全文：下载
作者：Yukitoshi Matsushita ; Yukitoshi Matsushita ; Taisuke Otsu 等
期刊名称：Econometrics Publications
印刷版ISSN：0969-4366
出版年度：2019
页码：1-28
出版社：Suntory Toyota International Centre for Economics and Related Disciplines
摘要：This paper sheds light on problems of statistical inference under alternative or nonstandard asymptotic frameworks from the perspective of jackknife empirical likelihood (JEL). Examples include small bandwidth asymptotics for semiparametric inference, many covariates asymptotics for regression models, and many-weak instruments asymptotics for instrumental variable regression. We first establish Wilks' theorem for the JEL statistic on a general semiparametric inference problem under the conventional asymptotics. We then show that the JEL statistics lose asymptotic pivotalness under the above nonstandard asymptotic frameworks, and argue that these phenomena are understood as emergence of Efron and Stein's (1981) bias of the jackknife variance estimator in the first order. Finally we propose a modification of JEL to recover asymptotic pivotalness under both the conventional and nonstandard asymptotics. Our modification works for all above examples and provides a unified framework to investigate nonstandard asymptotic problems.
关键词：jackknife ; empirical likelihood ; nonstandard asymptotics