On the local linear modelization of the nonparametric robust regression for functional time series data

In this work, we construct a robust nonparametric local linear estimator for a regression function when the regressors are a functional random variables by combining both Mestimation technique and an local linear ideas, we establish the almost complete convergence rate as well as the asymptotic normality of this estimator under an alpha-mixing assumption and on some topological characteristics of the data. Moreover, a simulation study is given in order to evaluate. on a finite sample, the performance of our estimator.