On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference
偏差估计对非参数推断覆盖精度的影响AI 解读 ↓
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偏差估计对非参数推断覆盖精度的影响
- 研究问题
- 核密度和局部多项式推断中，偏差校正如何影响置信区间覆盖误差，能否改善欠平滑方法对带宽选择的敏感性？
- 方法与思路
- 作者以新的学生化方式构造偏差校正区间，通过 Edgeworth 展开分析覆盖误差，推导最优带宽并用模拟说明。
- 材料陈述的贡献
- 摘要称在额外光滑性等条件下，适当学生化的偏差校正可改善覆盖误差，并给出内部点与边界点不同的带宽结论。
- 阅读关注点
- 应核对偏差估计的不确定性如何进入标准误，并区分二阶核、其他核及奇数阶局部多项式在内部和边界的结论。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审及期刊接收未核实；摘要未给具体展开条件，不能推断均方误差最优带宽普遍适用。
原文摘要
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 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.