Abstract This paper proposes five pointwise consistent and asymptotic normal estimators of the asymptotic variance function of the Nadaraya-Watson kernel estimator for nonparametric regression. The proposed estimators are constructed based on the first-stage nonparametric residuals, and their asymptotic properties are established under the assumption that the same bandwidth sequences are used throughout, which mimics what researchers do in practice while making derivations more complicated instead. A limited Monte Carlo experiment demonstrates that the proposed estimators possess smaller pointwise variability in small samples than the pair and wild bootstrap estimators which are commonly used in practice.

中文翻译：

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非参数回归的标准误差

摘要 本文提出了用于非参数回归的 Nadaraya-Watson 核估计量的渐近方差函数的五个逐点一致且渐近正态估计量。所提出的估计量是基于第一阶段非参数残差构建的，并且它们的渐近特性是在始终使用相同带宽序列的假设下建立的，这模仿了研究人员在实践中所做的事情，同时使推导变得更加复杂。有限的蒙特卡罗实验表明，与实践中常用的成对和野生引导估计器相比，所提出的估计器在小样本中具有更小的逐点变异性。