Nonparametric Quantile Regression Estimation for Functional Dependent Data

Abstract

Let (X i , Y i ) i=1,…, n be a sequence of strongly mixing random variables valued in ℱ × ℝ, where ℱ is a semi-metric space. We consider the problem of estimating the quantile regression function of Y i given X i . The principal aim of the article is to prove the consistency in L p norm of the proposed kernel estimate. The usefulness of the estimation is illustrated by a real data application where we are interested in forecasting hourly ozone concentration in the south-east of French.