Estimation in generalized linear models for functional data via penalized likelihood

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• 作者：Cardot ; Hervé ; Sarda ; Pacal
• 关键词：62G07 ; 62G12 ; 62G20 ; 65J20 ; Covariance operator ; Hilbert space valued random variables ; Ill-posed problem ; Regularization ; Splines
• 刊名：Journal of Multivariate Analysis
• 出版年：2005
• 期刊代码：77_0047259x
• 类别：mt
• 出版时间：January, 2005
• 卷：92
• 期：1
• 页码：24-41
• 文件大小：301 K

摘要

We analyze in a regression setting the link between a scalar response and a functional predictor by means of a Functional Generalized Linear Model. We first give a theoretical framework and then discuss identifiability of the model. The functional coefficient of the model is estimated via penalized likelihood with spline approximation. The L² rate of convergence of this estimator is given under smoothness assumption on the functional coefficient. Heuristic arguments show how these rates may be improved for some particular frameworks.