Estimation and Testing of Varying Coefficients in Quantile Regression

Abstract

In this article, we establish a novel connection between the null hypothesis H₀ on the coefficients and a rank-reducible form of the varying coefficient model in quantile regression. We use B-splines to approximate the varying coefficients in the rank-reducible model, and make use of the fact that the null hypothesis H₀ implies a unidimensional structure of a transformed coefficient matrix for the B-spline basis functions. By evaluating the unidimensional structure, we alleviate the difficulty of testing such hypotheses commonly considered in varying coefficient quantile models. We demonstrate through numerical studies that the proposed method can be much more powerful than the rank score test which is widely used in the quantile regression literature. Supplementary materials for this article are available online.

• Dimension reduction
• Hypothesis test
• Singular value decomposition.