Kernel Averaging Estimators
Kernel Averaging Estimators
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DOI：
10.1080/07350015.2021.2006668
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发表时间：
2021-11
影响因子：
3
通讯作者：
Rong Zhu;Xinyu Zhang;Alan T. K. Wan;Guohua Zou
中科院分区：
文献类型：
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作者：
Rong Zhu;Xinyu Zhang;Alan T. K. Wan;Guohua Zou
摘要带宽选择问题是一个基本的模型选择问题，源于回归平滑性的不确定性。在这篇文章中，我们提倡一种模型平均方法来规避这种不确定性所造成的问题。我们的新方法涉及平均在一系列的Nadaraya-Watson内核估计，每个不同的带宽下，与这些不同的估计的权重选择，使最小二乘交叉验证标准最小化。我们证明了所得的组合核估计达到最小可能的渐近总平方误差。在一个模拟研究和一个真实的数据例子中，证明了新的估计量的优越性，超过了在有限样本中被广泛接受的传统带宽选择的估计量。
Abstract The issue of bandwidth selection is a fundamental model selection problem stemming from the uncertainty about the smoothness of the regression. In this article, we advocate a model averaging approach to circumvent the problem caused by this uncertainty. Our new approach involves averaging across a series of Nadaraya-Watson kernel estimators each under a different bandwidth, with weights for these different estimators chosen such that a least-squares cross-validation criterion is minimized. We prove that the resultant combined-kernel estimator achieves the smallest possible asymptotic aggregate squared error. The superiority of the new estimator over estimators based on widely accepted conventional bandwidth choices in finite samples is demonstrated in a simulation study and a real data example.