On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference
On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference
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DOI：
10.1080/01621459.2017.1285776
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发表时间：
2018-01-01
影响因子：
3.7
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.
非参数方法在现代实证研究中起着核心作用。虽然他们提供的推理程序是更强大的参数误设定偏差，他们可能是相当敏感的调整参数的选择。我们研究了在核密度和局部多项式回归估计的背景下，偏差校正对置信区间覆盖的影响，并证明了偏差校正可以优先于欠平滑，以最大限度地减少覆盖误差，并增加调整参数选择的鲁棒性。这是使用一种新颖而简单的Studentization来实现的，它导致了一种新的构建基于内核的偏差校正置信区间的方法。此外，对于实际情况下，我们得出的覆盖误差的最佳带宽，并讨论易于实现的带宽选择器。对于内部点，我们表明，均方误差（MSE）的原始点估计（偏差校正前）的最佳带宽提供了最快的覆盖误差衰减率偏差校正后，二阶（等效）内核时，但否则是次优的，因为它是太“大”。最后，对于奇数次局部多项式回归，我们表明，与点估计一样，当使用适当的学生化时，覆盖误差会自动适应边界点;然而，原始点估计的MSE最优带宽是次优的。所有的结果都是建立在有效的Edgeworth展开，并与模拟数据。我们的研究结果有重要的影响，实证工作，因为它们表明，偏差校正的置信区间，加上适当的标准误差，有较小的覆盖误差和调整参数的选择，在实际相关的情况下，额外的平滑度是不太敏感的。
Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice. This is achieved using a novel, yet simple, Studentization, which leads to a new way of constructing kernel-based bias-corrected confidence intervals. In addition, for practical cases, we derive coverage error optimal bandwidths and discuss easy-to-implement bandwidth selectors. For interior points, we show that the mean-squared error (MSE)-optimal bandwidth for the original point estimator (before bias correction) delivers the fastest coverage error decay rate after bias correction when second-order (equivalent) kernels are employed, but is otherwise suboptimal because it is too "large." Finally, for odd-degree local polynomial regression, we show that, as with point estimation, coverage error adapts to boundary points automatically when appropriate Studentization is used; however, the MSE-optimal bandwidth for the original point estimator is suboptimal. All the results are established using valid Edgeworth expansions and illustrated with simulated data. Our findings have important consequences for empirical work as they indicate that bias-corrected confidence intervals, coupled with appropriate standard errors, have smaller coverage error and are less sensitive to tuning parameter choices in practically relevant cases where additional smoothness is available.