Some contributions to the estimation of models defined by conditional estimating equations.

Summary In this thesis, we study models defined by conditional moment equations. A large part of statistical models (regressions, quantile regressions, transformation models, instrumental variable models, etc.) can be defined in this form. We are interested in the case of models with a finite dimensional parameter to be estimated, as well as in the case of semi parametric models requiring the estimation of a finite dimensional parameter and an infinite dimensional parameter. In the class of semi-parametric models studied, we focus on models with a single revealing direction that achieve a compromise between simple and accurate parametric modeling, but too rigid and therefore exposed to model error, and non-parametric estimation, which is very flexible but suffers from the curse of dimension. In particular, we study these semi-parametric models in the presence of random censoring. The main thread of our study is a contrast in the form of a U-statistic, which allows to estimate the unknown parameters in general models.