Bootstrapping in Nonparametric Regression: Local Adaptive Smoothing and Confidence Bands
Bootstrapping in Nonparametric Regression: Local Adaptive Smoothing and Confidence Bands
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DOI：
10.1080/01621459.1988.10478572
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发表时间：
1988-03
影响因子：
3.7
通讯作者：
W. Härdle;A. Bowman
中科院分区：
文献类型：
--
作者：
W. Härdle;A. Bowman
摘要在非参数回归的背景下考虑自助法的操作。从估计的残差中获取引导样本，以研究适当重中心的核估计器的分布。研究了该原理在带宽局部自适应选择问题和置信度带构造中的应用，并与基于渐近均值和方差的直接方法进行了比较。自举的技术是用观测误差的经验分布函数来代替感兴趣的统计函数定义中的任何未知分布的出现。在回归环境中，这些误差不是直接观察到的，尽管它们可以通过来自拟合模型的残差来发挥作用。在本文中，拟合的模型是一个核心的非参数回归估计。由于涉及到非参数平滑，因此在平滑过程中产生的偏差会带来额外的困难。然而，这种偏见是可以估计的。
Abstract The operation of the bootstrap in the context of nonparametric regression is considered. Bootstrap samples are taken from estimated residuals to study the distribution of a suitably recentered kernel estimator. The application of this principle to the problem of local adaptive choice of bandwidth and to the construction of confidence bands is investigated and compared with a direct method based on asymptotic means and variances. The technique of the bootstrap is to replace any occurrence of the unknown distribution in the definition of the statistical function of interest by the empirical distribution function of the observed errors. In a regression context these errors are not directly observed, although their role can be played by the residuals from the fitted model. In this article the fitted model is a kernel nonparametric regression estimator. Since nonparametric smoothing is involved, an additional difficulty is created by the bias incurred in smoothing. This bias, however, can be estimated...