摘要翻译：
本文研究了随机抽样下非参数局部多项式回归方法的高阶推断性质。我们证明了$T$统计量的Edgeworth展开式和区间估计的复盖误差展开式，(i)在数据生成过程中一致成立，(ii)允许一致核，(iii)回归函数导数的复盖估计。高阶展开式的项及其作为样本量和带宽序列的函数的相关率取决于总体回归函数的光滑性、推论过程所利用的光滑性以及评价点是在支持的内部还是在支持的边界上。我们证明了在所有情况下，稳健的偏差校正置信区间具有最快的复盖误差衰减率，并且我们使用我们的结果来提供新颖的，推理最优的带宽选择器。主要的方法学结果在companion\textsf{R}和\textsf{Stata}软件包中实现。
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英文标题：
《Coverage Error Optimal Confidence Intervals for Local Polynomial
  Regression》
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作者：
Sebastian Calonico, Matias D. Cattaneo, Max H. Farrell
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最新提交年份：
2021
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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 studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for $t$ statistics and coverage error expansions for interval estimators that (i) hold uniformly in the data generating process, (ii) allow for the uniform kernel, and (iii) cover estimation of derivatives of the regression function. The terms of the higher-order expansions, and their associated rates as a function of the sample size and bandwidth sequence, depend on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point is in the interior or on the boundary of the support. We prove that robust bias corrected confidence intervals have the fastest coverage error decay rates in all cases, and we use our results to deliver novel, inference-optimal bandwidth selectors. The main methodological results are implemented in companion \textsf{R} and \textsf{Stata} software packages.
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PDF链接：
https://arxiv.org/pdf/1808.01398