Asymptotics for penalized spline estimators in quantile regression

Abstract

Quantile regression predicts the τ-quantile of the conditional distribution of a response variable given the explanatory variable for τ ∈ (0, 1). The aim of this paper is to establish the asymptotic distribution of the quantile estimator obtained by penalized spline method. A simulation and an exploration of real data are performed concerned with our results.