Functional data analysis: local linear estimation of the \(L_1\)-conditional quantiles

We consider a new estimator of the quantile function of a scalar response variable given a functional random variable. This new estimator is based on the \(L_1\) approach. Under standard assumptions, we prove the almost-complete consistency as well as the asymptotic normality of this estimator. This new approach is also illustrated through some simulated data and its superiority, compared to the classical method, has been proved for practical purposes.