Methodology and convergence rates for functional linear regression
Methodology and convergence rates for functional linear regression
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DOI：
10.1214/009053606000000957
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发表时间：
2007-02-01
影响因子：
4.5
通讯作者：
Horowitz, Joel L.
中科院分区：
文献类型：
--
作者：
Hall, Peter;Horowitz, Joel L.
在函数线性回归中，斜率“参数”是一个函数。因此，在非参数环境中，它由无限数量的未知数决定。它的估计涉及解决一个不适定的问题，并与一系列方法，包括统计平滑和反卷积的接触点。估计斜率函数的标准方法是明确地基于功能主成分分析，因此，在特征值和特征函数方面的谱分解。我们详细讨论了这种方法，并表明，在某些情况下，最佳的收敛速度实现的PCA技术。另一种方法的基础上二次正则化的建议，并从某些角度来看，具有优势。
In functional linear regression, the slope "parameter" is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of contact with a range of methodologies, including statistical smoothing and deconvolution. The standard approach to estimating the slope function is based explicitly on functional principal components analysis and, consequently, on spectral decomposition in terms of eigenvalues and eigenfunctions. We discuss this approach in detail and show that in certain circumstances, optimal convergence rates are achieved by the PCA technique. An alternative approach based on quadratic regularisation is suggested and shown to have advantages from some points of view.