G. Aneiros-perez, H. Cardot, G. Estevez-perez, and P. Vieu, Maximum ozone concentration forecasting by functional non-parametric approaches, Environmetrics, vol.3, issue.4, pp.675-685, 2004.
DOI : 10.1002/env.659

Y. Baraud, Model selection for regression on a random design, ESAIM: Probability and Statistics, vol.6, pp.127-146, 2002.
DOI : 10.1051/ps:2002007

A. Barron, L. Birgé, and P. Massart, Risk bounds for model selection via penalization. Probability Theory and Related Fields, pp.301-413, 1999.
DOI : 10.1007/s004400050210

L. Birgé and P. Massart, Minimum Contrast Estimators on Sieves: Exponential Bounds and Rates of Convergence, Bernoulli, vol.4, issue.3, pp.329-375, 1998.
DOI : 10.2307/3318720

D. Bosq, Linear Processes in Function Spaces, Lecture Notes in Statistics, vol.149, 2000.
DOI : 10.1007/978-1-4612-1154-9

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, 2011.
DOI : 10.1007/978-0-387-70914-7

T. Cai and P. Hall, Prediction in functional linear regression. The Annals of Statistics, pp.2159-2179, 2006.

H. Cardot, C. Crambes, and P. Sarda, Ozone pollution forecasting, Statistical methods for Biostatistics and Related Fields, pp.221-243, 2007.

H. Cardot, F. Ferraty, and P. Sarda, Functional linear model, Statistics & Probability Letters, vol.45, issue.1, pp.11-22, 1999.
DOI : 10.1016/S0167-7152(99)00036-X

H. Cardot, F. Ferraty, and P. Sarda, Spline estimators for the functional linear model, Statistica Sinica, vol.13, issue.3, pp.571-591, 2003.

H. Cardot and J. Johannes, Thresholding projection estimators in functional linear models, Journal of Multivariate Analysis, vol.101, issue.2, pp.395-408, 2010.
DOI : 10.1016/j.jmva.2009.03.001
URL : http://doi.org/10.1016/j.jmva.2009.03.001

H. Cardot, A. Mas, and P. Sarda, CLT in functional linear regression models. Probability Theory and Related Fields, pp.3-4, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00007772

L. Hengartner and N. W. , Cavalier Adaptive estimation for inverse problems with noisy operators, Inverse Problems, vol.21, issue.4, pp.1345-1361, 2005.

F. Comte and J. Johannes, Adaptive estimation in circular functional linear models, Mathematical Methods of Statistics, vol.19, issue.1, pp.42-63, 2010.
DOI : 10.3103/S1066530710010035
URL : https://hal.archives-ouvertes.fr/hal-00410729

F. Comte, Y. Rozenholc, and M. Taupin, Penalized contrast estimator for adaptive density deconvolution, Canadian Journal of Statistics, vol.18, issue.3, pp.431-452, 2006.
DOI : 10.1002/cjs.5550340305
URL : https://hal.archives-ouvertes.fr/hal-00016489

C. Crambes, A. Kneip, and P. Sarda, Smoothing splines estimators for functional linear regression. The Annals of Statistics, pp.35-72, 2009.
DOI : 10.1214/07-aos563
URL : https://hal.archives-ouvertes.fr/hal-00627068

S. Efromovich and V. Koltchinskii, On inverse problems with unknown operators, IEEE Transactions on Information Theory, vol.47, issue.7, pp.2876-2894, 2001.
DOI : 10.1109/18.959267

F. Ferraty and P. Vieu, Nonparametric Functional Data Analysis, 2006.

A. Goldenshluger and A. Tsybakov, Adaptive prediction and estimation in linear regression with infinitely many parameters, The Annals of Statistics, vol.29, issue.6, pp.1601-1619, 2001.

A. Goldenshluger and A. Tsybakov, Optimal prediction for linear regression with infinitely many parameters, Journal of Multivariate Analysis, vol.84, issue.1, pp.40-60, 2003.
DOI : 10.1016/S0047-259X(02)00006-4
URL : https://hal.archives-ouvertes.fr/hal-00103951

P. Hall and J. L. Horowitz, Methodology and convergence rates for functional linear regression. The Annals of Statistics, pp.70-91, 2007.
DOI : 10.1214/009053606000000957
URL : http://arxiv.org/abs/0708.0466

P. Hall and M. Hosseini-nasab, On properties of functional principal components analysis, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.57, issue.1, pp.109-126, 2006.
DOI : 10.1198/016214504000001745

P. R. Halmos, What does the spectral theorem say? The American Mathematical Monthly, pp.241-247, 1963.

M. Hoffmann and M. Reiss, Nonlinear estimation for linear inverse problems with error in the operator, The Annals of Statistics, vol.36, issue.1, pp.310-336, 2008.
DOI : 10.1214/009053607000000721
URL : https://hal.archives-ouvertes.fr/hal-00693076

Y. Li and T. Hsing, On rates of convergence in functional linear regression, Journal of Multivariate Analysis, vol.98, issue.9, pp.1782-1804, 2007.
DOI : 10.1016/j.jmva.2006.10.004

C. L. Mallows, Some comments on C p, Technometrics, vol.15, pp.661-675, 1973.
DOI : 10.2307/1267380

P. Massart, Concentration inequalities and model selection, volume 1896 of Lecture Notes in Mathematics, from the 33rd Summer School on Probability Theory held in Saint-Flour, 2003.

C. Preda and G. Saporta, PLS regression on a stochastic process, Computational Statistics & Data Analysis, vol.48, issue.1, pp.149-158, 2005.
DOI : 10.1016/j.csda.2003.10.003
URL : https://hal.archives-ouvertes.fr/hal-01124683

J. O. Ramsay and B. W. Silverman, Functional Data Analysis, 2005.

A. B. Tsybakov, Introduction à l'estimation non-paramétrique, Mathématiques & Applications, vol.41, 2004.

N. Verzelen, High-dimensional Gaussian model selection on a Gaussian design, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.46, issue.2, pp.480-524, 2010.
DOI : 10.1214/09-AIHP321
URL : https://hal.archives-ouvertes.fr/inria-00311412

M. Yuan and T. Cai, A reproducing kernel Hilbert space approach to functional linear regression. The Annals of Statistics, pp.3412-3444, 2010.