On the quantile regression when the regressor is functional: Spatial data case [Sur la régression quantile pour variable explicative fonctionnelle: Cas des données spatiales]

摘要

In this Note, we study the spatial relation between a real random variable Y and a functional variable X via conditional quantiles estimation. More precisely, we consider a random filed (Zi=(Xi,Yi)i∈NN,N≥1) with same law as (X, Y) and we establish the p-mean consistency of the kernel estimate of the conditional quantile of Y_i given X_i.