Coverage error optimal confidence intervals for local polynomial regression
Coverage error optimal confidence intervals for local polynomial regression
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DOI：
10.3150/21-bej1445
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发表时间：
2022-11-01
期刊：
影响因子：
1.5
通讯作者：
Farrell, Max H.
中科院分区：
文献类型：
--
作者：
Calonico, Sebastian;Cattaneo, Matias D.;Farrell, Max H.
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覆盖误差展开式，这些展开式(I)在数据生成过程中一致成立，(Ii)允许一致核，(Iii)覆盖回归函数的导数估计。高阶展开式的项及其关联率作为样本大小和带宽序列的函数，取决于总体回归函数的光滑性、推理过程所利用的光滑性以及评估点是在支撑点的内部还是在支撑点的边界上。我们证明了稳健的偏差校正置信度在所有情况下都具有最快的覆盖误差衰减率，并利用我们的结果来提供新颖的、推断最优的带宽选择器。主要的方法学结果在同伴R和STATA软件包中实现。
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 es-timators 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 associ-ated 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 R and Stata software packages.