Asymptotic normality of the local linear estimator of the functional expectile regression

We are concerned with the nonparametric estimation of the expectile functional regression. More precisely, we build an estimator, by the local linear smoothing approach, of the conditional expectile. Then we establish the asymptotic distribution of the constructed estimator. Establishing this result requires the Bahadur representation of the conditional expectile. The latter is obtained under certain standard conditions which cover the functional aspect of the data as well as the nonparametric characteristic of the model. The real impact of this result in nonparametric functional statistics has been discussed and highlighted using artificial data.