In this article, we propose nonparametric generalized method of moments estimation for nonparametric additive models with high order spatial autoregressive dependence. The estimation procedure is derived in three steps by combining a spline-backfitting method with generalized moment conditions that relieve correlations within the dependent variables. Consistency and asymptotic normality are demonstrated under mild conditions. Specifically, compared with estimators of nonparametric functions that ignore cross-sectional dependence in errors, the resultant estimators that consider the error term are asymptotically more efficient and achieve the well-known oracle properties. Simulation studies investigating the finite sample performance of the estimation procedure confirm the validity of our asymptotic theory. An application to the Boston housing data serves as a practical illustration.

中文翻译：

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具有高阶空间自回归误差的非参数加性模型的估计

在本文中，我们提出了具有高阶空间自回归相关性的非参数加性模型的非参数广义矩估计方法。通过将样条回拟合方法与广义矩条件相结合，可以在三个步骤中推导出估计过程，从而缓解因变量内的相关性。在温和条件下证明了一致性和渐近正态性。具体而言，与忽略误差中横截面相关性的非参数函数估计量相比，考虑误差项的合成估计量渐近更有效，并实现了众所周知的预言机属性。调查估计程序的有限样本性能的模拟研究证实了我们渐近理论的有效性。