On rates of convergence in functional linear regression

JOURNAL OF MULTIVARIATE ANALYSIS

卷:98

Article

Li, Yehua ; Hsing, Tailen

关键词: functional data analysis;    penalized least squares;    periodic spline;   

DOI  :  10.1016/j.jmva.2006.10.004

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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