In this thesis, we focus on the semi-parametric regression model y = f( \theta'x; \epsilon), where x \in R^p et y\in R. Our objective is to study problems of estimation of the parameters and f in this model with recursive methods. In the rst part, we develop an approach which is based on a method introduced by Li (1991), called Sliced Inverse Regression (SIR). We propose recursive sirmethods for estimating the parameter . In the particular case when the number of slices equal to 2, it is possible to obtain an analytic expression of the estimator of the direction . We propose a recursive form for this estimator, and a recursive estimation of the matrix of interest. Moreover, we propose an estimator of the direction of based on the use of only one \optimal" slice chosen among any number of slices. We call this new method SIRoneslice. We also o er a standard \naive bootstrap" for the choice of the number of slices. We establish somme asymtotic properties of the estimators and a simulation study illustrates the good numerical behavior of the estimators proposed. The recursive approach (SIR and SIRoneslice) has the advantage to be computationaly faster than the non recursive. In the second part, we work on data measured on bivalves. On these data, we compare the numerical behavior of three nonparametric estimators of the regression function : Nadaraya-Watson, recursive Nadaraya-Watson and R ev esz which is also recursive. In the last part of this thesis, we propose a method which combines the recursive estimation of the link function f by the recursive Nadaraya-Watson estimator and recursive estimation of parameter via the recursive SIR estimator. We establish a law of large numbers and a central limit theorem. We illustrate these theoretical results by simulations showing the good numerical behavior of the proposed estimation method.
