# Estimation of the Functional Linear Regression with Smoothing Splines

• Christophe Crambes
• Alois Kneip
• Pascal Sarda
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

We consider functional linear regression where a real variable Ydepends on a functional variable X. The functional coeficient of the model is estimated by means of smoothing splines. We derive the rates of convergence with respect to the semi-norm induced by the covariance operator of X, which comes to evaluate the error of prediction. These rates, which essentially depend on the smoothness of the function parameter and on the structure of the predictor, are shown to be optimal over a large class of functions parameters and distributions of the predictor.

## Keywords

Function Parameter Covariance Operator Functional Data Analysis Functional Principal Component Natural Spline
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Christophe Crambes
• 1
• Alois Kneip
• 2
• Pascal Sarda
• 3
1. 1.Montpellier II, place Eugène BataillonFrance
2. 2.Universität BonnGermany
3. 3.Institut de Mathématiques de Toulouse Equipe LSPUniversité Paul SabatierFrance