Test for single-index composite quantile regression

Abstract

It is known that composite quantile regression estimator could be much more efficient and sometimes arbitrarily more efficient than the least squares estimator. In this paper, tests for the index parameter and index function in the single-index composite quantile regression are considered. The asymptotic behaviors of the proposed tests are established and their limiting null distributions are demonstrated to follow an asymptotically χ 2 -distribution. The simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods.