Jackknife, small bandwidth and high-dimensional asymptotics

Yukitoshi Matsushita and Taisuke Otsu

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: 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.

Keywords: Jackknife; Empirical likelihood; Nonstandard asymptotics (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Date: 2019-07
New Economics Papers: this item is included in nep-ecm and nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:605

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