摘要翻译:
本文给出了一个统一的二阶渐近框架,用于推导形式为$\phi(\theta_0)$的参数,其中$\theta_0$是未知的,但可以用$\hat\theta_n$估计,并且$\phi$是一个在$\theta_0$处允许零一阶导数的已知映射。对于文献中的大量例子,二阶Delta方法揭示了插件估计量$\phi(\hat\theta_n)$的非退化弱极限。然而,我们证明了在正则性条件下,标准引导是一致的当且仅当二阶导数$\phi_{\theta_0}“=0$,即当$\phi_{\theta_0}”\neq0$时,标准引导是不一致的,并提供了无助于推理的退化极限。因此,我们确定了与Fang and Santos(2018)不同的引导失败的来源,因为即使$\phi$是可微的,问题(一致引导\textIt{nondegenerate}限制)仍然存在。我们证明了Babu(1984)中的校正程序可以推广到我们的一般设置。另外,当映射是二阶不可微的时,提出了一种改进的引导程序。两者都显示在某些条件下提供局部大小控制。作为一个例子,我们提出了一个公共条件异方差(CH)特征的检验,一个同时具有退化性和不可微性的设置--后者是因为雅可比矩阵在零处退化,并且我们允许多个公共CH特征的存在。
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英文标题:
《Inference on Functionals under First Order Degeneracy》
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作者:
Qihui Chen and Zheng Fang
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最新提交年份:
2019
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分类信息:
一级分类:Economics 经济学
二级分类:Econometrics 计量经济学
分类描述:Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论,微观计量经济学,宏观计量经济学,通过新方法发现的经济关系的实证内容,统计推论应用于经济数据的方法论方面。
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一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
This paper presents a unified second order asymptotic framework for conducting inference on parameters of the form $\phi(\theta_0)$, where $\theta_0$ is unknown but can be estimated by $\hat\theta_n$, and $\phi$ is a known map that admits null first order derivative at $\theta_0$. For a large number of examples in the literature, the second order Delta method reveals a nondegenerate weak limit for the plug-in estimator $\phi(\hat\theta_n)$. We show, however, that the `standard' bootstrap is consistent if and only if the second order derivative $\phi_{\theta_0}''=0$ under regularity conditions, i.e., the standard bootstrap is inconsistent if $\phi_{\theta_0}''\neq 0$, and provides degenerate limits unhelpful for inference otherwise. We thus identify a source of bootstrap failures distinct from that in Fang and Santos (2018) because the problem (of consistently bootstrapping a \textit{nondegenerate} limit) persists even if $\phi$ is differentiable. We show that the correction procedure in Babu (1984) can be extended to our general setup. Alternatively, a modified bootstrap is proposed when the map is \textit{in addition} second order nondifferentiable. Both are shown to provide local size control under some conditions. As an illustration, we develop a test of common conditional heteroskedastic (CH) features, a setting with both degeneracy and nondifferentiability -- the latter is because the Jacobian matrix is degenerate at zero and we allow the existence of multiple common CH features.
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PDF链接:
https://arxiv.org/pdf/1901.04861