数据投影加性模型中的局部线性平滑
Local linear smoothing in additive models as data projection
摘要：
讨论了可加非参数模型的局部线性光滑后拟合。这个过程是众所周知的，在适当的平滑条件下实现最佳的收敛速度。特别是，它允许估计的每个组件的添加剂模型具有相同的渐近精度，如果其他组件是已知的。局部线性平滑回拟的渐进讨论相当复杂，因为详细讨论通常需要压倒性的符号。在本文中，我们解释了当地的线性光滑回拟合估计作为一个投影的数据到一个线性空间与适当选择的半范数。这种方法既简化了数学讨论，也简化了对该版本的平滑后拟合特性的直观理解。
英文摘要：
We discuss local linear smooth backfitting for additive non-parametric models. This procedure is well known for achieving optimal convergence rates under appropriate smoothness conditions. In particular, it allows for the estimation of each component of an additive model with the same asymptotic accuracy as if the other components were known. The asymptotic discussion of local linear smooth backfitting is rather complex because typically an overwhelming notation is required for a detailed discussion. In this paper we interpret the local linear smooth backfitting estimator as a projection of the data onto a linear space with a suitably chosen semi-norm. This approach simplifies both the mathematical discussion as well as the intuitive understanding of properties of this version of smooth backfitting.
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