Varying-Coefficient Functional Linear Regression Models |
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Authors: | Hervé Cardot Pascal Sarda |
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Institution: | 1. Institut de Mathématiques de Bourgogne, Université de Bourgogne , Dijon, France Herve.Cardot@u-bourgogne.fr;3. Institut de Mathématiques de Toulouse, Université Paul Sabatier , Toulouse, France |
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Abstract: | This article considers a generalization of the functional linear regression in which an additional real variable influences smoothly the functional coefficient. We thus define a varying-coefficient regression model for functional data. We propose two estimators based, respectively, on conditional functional principal regression and on local penalized regression splines and prove their pointwise consistency. We check, with the prediction one day ahead of ozone concentration in the city of Toulouse, the ability of such nonlinear functional approaches to produce competitive estimations. |
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Keywords: | B-splines Conditional covariance function Conditional principal components regression Ill-posed problem Penalization |
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