On rates of convergence in functional linear regression
On rates of convergence in functional linear regression
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DOI：
10.1016/j.jmva.2006.10.004
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发表时间：
2007-10-01
影响因子：
1.6
通讯作者：
Hsing, Tailen
中科院分区：
文献类型：
--
作者：
Li, Yehua;Hsing, Tailen
本文研究了泛函线性回归模型中回归权函数估计的收敛速度。假设预测器以及权函数在边界点处的导数相等的意义上是平滑的和周期性的。假设函数数据是在具有测量误差的离散点上观测的，采用复傅立叶基估计真实数据，并基于惩罚最小二乘准则建立回归权函数。然后推导出这两个估计量的收敛速度。一个模拟研究也提供了说明我们的方法的数值性能，并与主成分回归方法进行比较。(c)2006年爱思唯尔公司All rights reserved.
This paper investigates the rate of convergence of estimating the regression weight function in a functional linear regression model. It is assumed that the predictor as well as the weight function are smooth and periodic in the sense that the derivatives are equal at the boundary points. Assuming that the functional data are observed at discrete points with measurement error, the complex Fourier basis is adopted in estimating the true data and the regression weight function based on the penalized least-squares criterion. The rate of convergence is then derived for both estimators. A simulation study is also provided to illustrate the numerical performance of our approach, and to make a comparison with the principal component regression approach. (c) 2006 Elsevier Inc. All rights reserved.