Estimation non paramétrique pour des données fonctionnelles et tronquées.

Abstract

The study of a link between two variables was and still a challenge for a lot of researchers in many fields of application and as in many of these fields appear functional data, we find many works have been devoted in this axis. In this thesis, we propose nonparametric estimators of two functions used in prevision problem ; the generalised regression function, which is a generalization of the regression function based on the conditional expectation and the conditional quantile. During these studies we have always assumed that the response variable is real and is subjected to a left-truncation while the explanatory variable is functional, i.e with values in a space of infinite dimension. We used a functional locally linear modeling for the estimation of the two functions by considering a local linear estimator adapted to a polynomial of one degree. Almost sur pointwise and uniform convergences with rates have been established for each estimator and simulation studies have been carried out to reinforce the efficiency of the proposed estimators on examples.