This thesis is devoted to the study of some semi-parametric deformation models.Our aim is to provide recursive methods, related to stochastic algorithms, in order to estimate the different parameters of the models. In the first part, we present the theoretical tools which we will use in the next part. On the one hand, we focus on stochastic approximation methods, in particular the Robbins-Monro algorithm and the Kiefer-Wolfowitz algorithm. On the other hand, we introduce kernel estimators in order to estimate a probability density function and a regression function. More particularly, we present the two most famous kernel estimators which are the one of Parzen-Rosenblatt and the one of Nadaraya-Watson. We also present their recursive version.In the second part, we present the results we obtained in this thesis.Firstly, we provide a recursive estimation method of the shift parameter and the regression function for the translation model in which the regression function is periodic. Secondly, we extend this estimation procedure to the shape invariant model, providing estimation of the height parameter, the translation parameter and the scale parameter, as well as the common shape function.Thirdly, we are interested in the parametric deformation model of random variables where the deformation is known and depending on an unknown parameter.For these three models, we establish the almost sure convergence and the asymptotic normality of each estimator. Finally, we numerically illustrate the asymptotic behaviour of our estimators on simulated data and on real data.
