Nonparametric estimation of functional and censored data.

Abstract

In this thesis, we consider the problem of the nonparametric estimation of the regression function when the response variable is real and the regressor is valued in a functional space (space of infinite dimension), by using the local linear method. Firstly, we suppose that the observations are strongly mixing and we establish the pointwise and the uniform almost complete convergence, with rates, of the local linear regression estimator. Secondly, we consider a sequence of independent and identically distributed observations and we introduce a local linear nonparametric estimation of the regression function for a censored scalar response random variable. Then, we establish their pointwise and the uniform almost-complete convergences, with rates. Our main results is based on the functional and censored data under strong mixing condition and we study the rate of the pointwise almostcomplete convergence of the local linear regression estimator. Finally, a simulation study illustrates the performance of the local linear methodology with respect to other kernel method, in the tree cases: Functional and complete case under dependent condition, Functional and censored case under independent condition and Functional and censored case under dependent condition.