Jackknife, small bandwidth and high-dimensional asymptotics
Jackknife, small bandwidth and high-dimensional asymptotics
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发表时间：
2019-07
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通讯作者：
Yukitoshi Matsushita;Taisuke Otsu
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作者：
Yukitoshi Matsushita;Taisuke Otsu
本文从刀切经验似然（JEL）的角度出发，研究了在替代或非标准渐近框架下的统计推断问题。例子包括半参数推断的小带宽渐近性，回归模型的多协变量渐近性，以及工具变量回归的多弱工具渐近性。本文首先建立了关于一般半参数推断问题的JEL统计量在常规渐近下的Wilks定理。然后我们证明了JEL统计量在上述非标准渐近框架下失去了渐近稳定性，并认为这些现象可以理解为一阶刀切方差估计的Efron和Stein（1981）偏差的出现。最后，我们提出了一个修改的JEL恢复渐近稳定性下的常规和非标准渐近。我们的修改适用于所有上述例子，并提供了一个统一的框架来研究非标准渐近问题。
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.