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Jackknife, small bandwidth and high-dimensional asymptotics

Author

Listed:
  • Yukitoshi Matsushita
  • Taisuke Otsu

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.

Suggested Citation

  • Yukitoshi Matsushita & Taisuke Otsu, 2019. "Jackknife, small bandwidth and high-dimensional asymptotics," STICERD - Econometrics Paper Series 605, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  • Handle: RePEc:cep:stiecm:605
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    File URL: http://sticerd.lse.ac.uk/dps/em/em605.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Jackknife; Empirical likelihood; Nonstandard asymptotics;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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