Estimation and testing for varying-coefficient single-index quantile regression models

In this paper we propose varying-coefficient single-index quantile regression models, which includes most existing quantile regression models. We adopt B-spline basis approximation for the estimation of nonparametric components and use the “delete-one-component” method to construct check loss function. Under some mild conditions, we establish asymptotic theory of the proposed estimators for both the parametric and nonparametric components. Moreover, we propose a rank score based test to examine whether the varying-coefficient functions are constant. The finite sample performance of the proposed estimation method is illustrated by simulation studies and an empirical analysis of two real datasets.