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.