Functional quantile regression: local linear modelisation

A nonparametric local linear estimator of the conditional quantiles of a scalar response variable Y given a random variable X taking values in a semi-metric space. We establish the almost complete consistency and the asymptotic normality of this estimate. We prove that the asymptotic proprieties of this estimate are closely related to some topological characteristics of the data. Finally, a Monte Carlo study is carried out to evaluate the performance of this estimate.