Abstract
The problem of estimating the spatio-functional quantile regression for a given spatial mixing structure (Xi,Yi)∈F×R, when i∈ZN, N≥1 and F is a separable Hilbert space, is investigated. We construct and compare four estimators of the regression quantile. The proposed estimators cover the two main aspects of the statistical analysis, namely the parametric and nonparametric approaches. Precisely, using a parametric approach, we construct two estimators that are based respectively on the B-spline smoothing and the PCA regression. The other two estimators are constructed by using a non-parametric approach, namely the local constants method and the local linear method. Then, we establish the asymptotic properties of the four constructed estimators, and we examine their feasibility for finite size samples (i) on simulated data, and (ii) on real climatological data, which confirm the usefulness of our methodologies in practice.