Simultaneous bootstrap confidence bands in nonparametric regression
Simultaneous bootstrap confidence bands in nonparametric regression
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DOI：
10.1080/10485259808832748
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发表时间：
1998-01-01
影响因子：
1.2
通讯作者：
Polzehl, J
中科院分区：
文献类型：
--
作者：
Neumann, MH;Polzehl, J
本文构造了非参数回归的渐近置信带。我们的假设涵盖了观测值的不等方差和非均匀的、可能相当聚集的设计。置信带是基于一个欠光滑的局部多项式估计量，通过野自举得到一个合适的分位数。我们推导了覆盖概率误差的一定比率（在样本量n中），这改进了依赖于某些高斯过程最大值的渐近分布的现有方法的结果，我们提出了一个实用的基于数据的带宽选择规则。一项小型模拟研究说明了我们的方法比其他常用方法可能获得的好处。
In the present paper we construct asymptotic confidence bands in non-parametric regression. Our assumptions cover unequal variances of the observations and nonuniform, possibly considerably clustered design. The confidence band is based on an undersmoothed local polynomial estimator, An appropriate quantile is obtained via the wild bootstrap. We derive certain rates (in the sample size n) for the error in coverage probability, which improves on existing results for methods that rely on the asymptotic distribution of the maximum of some Gaussian process, We propose a practicable rule for a data-dependent choice of the band-width. A small simulation study illustrates the possible gains by our approach over alternative frequently used methods.