U. Anders, Neural network pruning and statistical hypotheses tests, Progress in Connectionnist-Based Information Systems (Addendum) Proceedings of ICONIP'97, pp.1-4, 1997.

U. Anders and O. Korn, Model selection in neural networks, Neural Networks, vol.12, issue.2, pp.309-323, 1999.
DOI : 10.1016/S0893-6080(98)00117-8

A. Antoniadis, J. Berruyer, and R. Carmona, Régression non linéaire et applications, 1992.

D. M. Bates and D. G. Watts, Nonlinear regression analysis and its applications, 1988.
DOI : 10.1002/9780470316757

M. Bishop, Neural Networks for Pattern Recognition, 1995.

W. Buntine and A. Weigend, Computing second derivatives in feed-forward networks: a review, IEEE Transactions on Neural Networks, vol.5, issue.3, pp.480-488, 1994.
DOI : 10.1109/72.286919

S. Chen, A. Billings, and W. Luo, Orthogonal least squares methods and their application to non-linear system identification, International Journal of Control, vol.10, issue.5, pp.1873-1896, 1989.
DOI : 10.2307/2284566

B. Efron and R. J. Tibshirani, An introduction to the bootstrap, 1993.
DOI : 10.1007/978-1-4899-4541-9

S. E. Fahlman and C. Lebière, The cascade correlation learning architecture, Advances in Neural Information Processing Systems 2, pp.524-532, 1990.

J. H. Friedman, An overview of predictive learning and function approximation, " in From Statistics to Neural Networks: Theory and Pattern Recognition, ASI Proc., Subseries F, 1994.

G. C. Goodwin and R. L. Payne, Dynamic system identification; experiment design and data analysis, 1977.

L. K. Hansen and J. Larsen, Linear unlearning for cross validation Advances in computational mathematics, pp.296-280, 1993.

B. Hassibi and D. Stork, Second order derivatives for network pruning: optimal brain surgeon, Advances in Neural Information Processing Systems 5, pp.164-171, 1993.

B. Hassibi, D. Stork, G. Wolff, and T. Watanabe, Optimal brain surgeon: Extensions and performance comparisons, Advances in Neural Information processing Systems 6, pp.263-270, 1994.

T. Heskes, Practical confidence and prediction intervals, Advances in Neural Information Processing Systems 9, pp.176-182, 1997.

T. Y. Kwok and D. Y. Yeung, Constructive algorithms for structure learning in feedforward neural networks for regression problems, IEEE Transactions on Neural Networks, vol.8, issue.3, pp.630-645, 1997.
DOI : 10.1109/72.572102

L. Cun, J. S. Denker, and S. A. Solla, Optimal brain damage, Advances in Neural Information Processing Systems, pp.598-605, 1990.

I. J. Leontaritis and S. A. Billings, Model selection and validation methods for non-linear systems, International Journal of Control, vol.2, issue.1, pp.311-341, 1987.
DOI : 10.1080/00207177708922285

J. C. Mackay, Bayesian Interpolation, Neural Computation, vol.49, issue.3, pp.415-447, 1992.
DOI : 10.1093/comjnl/11.2.185

D. J. Mackay, A Practical Bayesian Framework for Backpropagation Networks, Neural Computation, vol.4, issue.3, pp.448-472, 1992.
DOI : 10.1038/323533a0

D. J. Mackay, Comparison of Approximate Methods for Handling Hyperparameters, Neural Computation, vol.39, issue.5, pp.1035-1068, 1999.
DOI : 10.1007/BF01437407

M. Minoux, Programmation mathématique; théorie et algorithmes, 1983.

J. Moody, Prediction risk and architecture selection for neural networks, " in From statistics to neural networks: theory and pattern recognition applications, NATO ASI Series, 1994.

G. Paass, Assessing and improving neural network predictions by the bootstrap algorithm, Advances in Neural Information Processing Systems, pp.186-203, 1993.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C, 1992.

R. Reed, Pruning algorithms-a survey, IEEE Transactions on Neural Networks, vol.4, issue.5, pp.740-747, 1993.
DOI : 10.1109/72.248452

A. N. Refenes, A. D. Zapranis, J. Utans, and J. , Neural model identification, variable selection and model adequacy, Decision technologies for financial engineering, pp.243-261, 1997.
DOI : 10.1002/(SICI)1099-131X(199909)18:5<299::AID-FOR725>3.0.CO;2-T

B. D. Ripley, Pattern recognition and neural networks, 1995.
DOI : 10.1017/CBO9780511812651

I. Rivals and L. Personnaz, Construction of confidence intervals in neural modeling using a linear Taylor expansion, Proceedings of the International Workshop on Advanced Black-Box Techniques for Nonlinear Modeling, pp.8-10, 1998.

I. Rivals and L. Personnaz, On Cross Validation for Model Selection, Neural Computation, vol.11, issue.4, pp.863-870, 1999.
DOI : 10.1162/neco.1996.8.7.1421

I. Rivals, I. , and L. Personnaz, Construction of confidence intervals for neural networks based on least squares estimation, Neural Networks, vol.13, issue.4-5, pp.80-90, 2000.
DOI : 10.1016/S0893-6080(99)00080-5

URL : https://hal.archives-ouvertes.fr/hal-00798661

I. Rivals, I. , and L. Personnaz, A statistical procedure for determining the optimal number of hidden neurons of a neural model, Proceedings of the Second International Symposium on Neural Computation (NC'2000), 2000.

S. Saarinen, R. Bramley, and G. Cybenko, Ill-Conditioning in Neural Network Training Problems, SIAM Journal on Scientific Computing, vol.14, issue.3, pp.693-714, 1993.
DOI : 10.1137/0914044

G. A. Seber, Linear regression analysis, 1977.
DOI : 10.1002/9780471722199

G. A. Seber and C. Wild, Nonlinear regression, 1989.
DOI : 10.1002/0471725315

J. Sussman, Uniqueness of the weights for minimal feedforward nets with a given input-output map, Neural Networks, vol.5, issue.4, pp.589-593, 1992.
DOI : 10.1016/S0893-6080(05)80037-1

D. Urbani, P. Roussel-ragot, L. Personnaz, G. Dreyfus, and G. , The selection of neural models of non-linear dynamical systems by statistical tests, Neural Networks for Signal Processing, Proceedings of the 1994 IEEE Workshop, 1994.

H. White, Learning in Artificial Neural Networks: A Statistical Perspective, Neural Computation, vol.36, issue.4, pp.425-464, 1989.
DOI : 10.2307/1912526

G. Zhou and J. Si, A Systematic and Effective Supervised Learning Mechanism Based on Jacobian Rank Deficiency, Neural Computation, vol.10, issue.4, pp.1031-1045, 1998.
DOI : 10.1109/72.80202