Jackknife empirical likelihood: small bandwidth, sparse network and high-dimension asymptotic

Yukitoshi Matsushita and Taisuke Otsu

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: This paper sheds light on inference problems for statistical models under alternative or nonstandard asymptotic frameworks from the perspective of jackknife empirical likelihood. Examples include small bandwidth asymptotics for semiparametric inference and goodness-of- fit testing, sparse network asymptotics, many covariates asymptotics for regression models, and many-weak instruments asymptotics for instrumental variable regression. We first establish Wilks’ theorem for the jackknife empirical likelihood statistic on a general semiparametric in- ference problem under the conventional asymptotics. We then show that the jackknife empirical likelihood statistic may 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 modi- fication of the jackknife empirical likelihood 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.

JEL-codes: C1 (search for similar items in EconPapers)
Date: 2020-10-05
New Economics Papers: this item is included in nep-ecm and nep-ore
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Published in Biometrika, 5, October, 2020. ISSN: 0006-3444

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