摘要翻译：
给定一个数据集(t_i,y_i)，i=1,...,n,t_i在[0,1]中，非参数回归研究了如何指定一个合适的函数f_n:[0,1]->R，使数据可以由点(t_i,f_n(t_i))，i=1,...,n合理地近似。如果一个数据集表现出局部行为的大变化，例如光谱数据中的大峰，那么该方法必须能够适应平滑度的局部变化。虽然许多方法能够实现这一点，但它们在调整导数方面不太成功。本文给出了如何用加权光滑样条函数以简单的方式实现函数及其一阶和二阶导数的局部自适应的目标。采用基于残差的逼近概念，使回归函数具有局部自适应能力，并采用全局正则化方法，使回归函数在逼近约束下尽可能光滑。
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英文标题：
《Approximating Data with weighted smoothing Splines》
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作者：
P.L. Davies, M. Meise
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最新提交年份：
2009
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
  Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i, f_n(t_i)), i=1,..., n. If a data set exhibits large variations in local behaviour, for example large peaks as in spectroscopy data, then the method must be able to adapt to the local changes in smoothness. Whilst many methods are able to accomplish this they are less successful at adapting derivatives. In this paper we show how the goal of local adaptivity of the function and its first and second derivatives can be attained in a simple manner using weighted smoothing splines. A residual based concept of approximation is used which forces local adaptivity of the regression function together with a global regularization which makes the function as smooth as possible subject to the approximation constraints.
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PDF链接：
https://arxiv.org/pdf/712.1692