Estimation in generalized linear models for functional data via penalized likelihood |
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Authors: | Hervé Cardot,Pacal Sarda |
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Affiliation: | a Unité Biométrie et Intelligence Artificielle, INRA Toulouse, BP 27, 31326 Castanet-Tolosan Cedex, France b Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 31062 Toulouse Cedex, France |
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Abstract: | 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. |
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Keywords: | 62G07 62G12 62G20 65J20 |
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