L’approche neuronale de l’inférence statistique

Abstract

This thesis is an attemp t to contribute, even slightly, in situating the neural networks theory into the framework of applied statistics. Th e central issue of statistical inference was s tudied under the light of neural ap proach. A lot of attention was payed to the notion of generalization, with the aim to con cei ve an uni fied approach, ghattering toghether traditional statistical metho ds with those resulting from neural networks theory, and presenting them as emerging from the same principle. The comp etitor estimators to the least squares one are surveyed, this is also done for the different neural techniques conceived for the needs of regression and prediction. A comparative study was done with the aim to show that the fondamental concept, at the level of the ro ots, of these different metho ds can b e seen as u nique