Jackknife empirical likelihood: small bandwidth, sparse network and high-dimensional asymptotics
Jackknife empirical likelihood: small bandwidth, sparse network and high-dimensional asymptotics
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DOI：
10.1093/biomet/asaa081
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发表时间：
2020-10
期刊：
影响因子：
2.7
通讯作者：
Yukitoshi Matsushita;Taisuke Otsu
中科院分区：
文献类型：
--
作者：
Yukitoshi Matsushita;Taisuke Otsu
本文从折刀经验似然的角度出发，研究了统计模型在可选或非标准渐近框架下的推理问题。例子包括半参数推理和优度检验的小带宽渐近性、稀疏网络渐近性、回归模型的多协变量渐近性和工具变量回归的多弱工具渐近性。本文首先建立了一般半参数推理问题在常规渐近条件下的叠刀经验似然统计量的Wilks定理。然后，我们证明了在上述非标准渐近框架下，叠刀经验似然统计量可能会失去渐近关键性，并认为这些现象可以理解为一阶叠刀方差估计量的Efron和Stein（1981）偏差的出现。最后，我们提出了在常规和非标准渐近条件下恢复渐近枢轴性的刀切经验似然的一个修正。我们的改进适用于上述所有例子，并为研究非标准渐近问题提供了一个统一的框架。
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-offit 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 inference 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 modification 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.