Abstract

The confidence band of functions is complicated by the over-smoothing problem and the residual distribution. In this paper, we use bootstrap and data-sharpening methods to establish a general confidence band. The construction is simple and the band is narrower than existing estimation methods. At the same time, a technique based on quantiles makes the confidence band more controllable and damps down the stochastic error term. Afterwards, we conduct a limited simulation to illustrate that the proposed band performs better than existing ones. Finally, we show the theoretical properties of the results and prove them.

中文翻译：

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回归置信带中的数据锐化方法

摘要

函数的置信带因过度平滑问题和残差分布而变得复杂。在本文中，我们使用引导和数据锐化方法来建立一般置信带。构造简单，频带比现有的估计方法窄。同时，基于分位数的技术使置信带更加可控，并抑制了随机误差项。之后，我们进行了有限的模拟，以说明所提议的频段比现有频段表现更好。最后，我们展示了结果的理论性质并证明了它们。