The bootstrap in kernel regression for stationary ergodic data when both response and predictor are functions
The bootstrap in kernel regression for stationary ergodic data when both response and predictor are functions
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DOI：
10.1016/j.jmva.2019.05.004
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发表时间：
2018-06
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通讯作者：
Johannes T. N. Krebs
中科院分区：
文献类型：
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作者：
Johannes T. N. Krebs
考虑双函数回归模型Y= r（X）+ ε，其中响应变量Y是Hilbert空间值，协变量X在伪度量空间中取值.数据满足遍历性标准，该标准可以追溯到Laib和Louani（2010），并以三角形阵列排列。因此，我们的模型也适用于从空间过程中获得的样本，例如，平稳随机场。研究了算子r的Nadaraya-Watson型核估计，并得到了它的极限律，它是Hilbert空间上的高斯算子.此外，我们调查了一个天真的和野生的自举过程中的双功能设置，并证明其渐近有效性。这非常有用，因为基于渐进高斯分布建立置信集通常很困难。
We consider the double functional regression model Y= r (X)+ ε, where the response variable Y is Hilbert space-valued and the covariate X takes values in a pseudometric space. The data satisfy an ergodicity criterion which dates back to Laib and Louani (2010) and are arranged in a triangular array. So our model also applies to samples obtained from spatial processes, eg, stationary random fields. We study a kernel estimator of the Nadaraya–Watson type for the operator r and derive its limiting law which is a Gaussian operator on the Hilbert space. Moreover, we investigate both a naive and a wild bootstrap procedure in the double functional setting and demonstrate their asymptotic validity. This is quite useful as building confidence sets based on an asymptotic Gaussian distribution is often difficult.