论文标题
作为数据投影的添加模型中的本地线性平滑
Local linear smoothing in additive models as data projection
论文作者
论文摘要
我们讨论了添加剂非参数模型的本地线性平滑回合。该程序以在适当的平滑度条件下达到最佳收敛速率而闻名。特别是，它允许估算与已知其他组件相同的渐近精度的加性模型的每个组件。对局部线性平滑背贴的渐近讨论相当复杂，因为通常需要进行详细讨论的压倒性符号。在本文中，我们将局部线性平滑背贴估计量解释为数据投影在具有适当选择的半符号的线性空间上。这种方法简化了数学讨论，也简化了对这一版本的平滑背贴的属性的直观理解。
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.
