A smooth simultaneous confidence band (SCB) is constructed for the distribution of unobserved errors in a nonparametric regression model based on a plug-in kernel distribution estimator. The normalized estimation error process is shown to converge to a Gaussian process. Simulation experiments indicate that the proposed SCB not only strikes an intelligent balance between coverage probability and precision, but also achieves surprisingly as much as double efficiency of the classical infeasible SCB. Furthermore, extensive empirical studies are carried out to compare the proposed method with the smooth residual bootstrap method in order to demonstrate the usefulness of each of these methods. As an illustration, the proposed SCB is applied to the Old Faithful geyser data for testing the error distribution.

中文翻译：

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非参数回归中误差分布函数的平滑同时置信带

为基于插件核分布估计器的非参数回归模型中未观察到的误差分布构建了一个平滑的同时置信带 (SCB)。归一化估计误差过程显示为收敛到高斯过程。仿真实验表明，所提出的 SCB 不仅在覆盖概率和精度之间取得了智能平衡，而且令人惊讶地实现了经典不可行 SCB 的两倍效率。此外，还进行了广泛的实证研究，将所提出的方法与平滑残差自举法进行比较，以证明每种方法的有效性。例如，建议的 SCB 应用于老忠实间歇泉数据以测试误差分布。