Test for single-index composite quantile regression

It is known that composite quantile regression estimator could be muchmore efficient and sometimes arbitrarily more efficient than the leastsquares estimator. In this paper, tests for the index parameter andindex function in the single-index composite quantile regression areconsidered. The asymptotic behaviors of the proposed tests are established and their limiting null distributions are demonstrated to followan asymptotically χ2-distribution. The simulation studies and a realdata application are conducted to illustrate the finite sample performance of the proposed methods.&nbsp