a b s t r a c tIn this paper, we extend the composite quantile regression (CQR) method to a single-index model. The unknown link function is estimated by local composite quantile regression and the parametric index is estimated through the linear composite quantile. It is shown that the proposed estimators are consistent and asymptotically normal. The simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.

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It is known that composite quantile regression (CQR) could be much more efficient and sometimes arbitrarily more efficient than the least squares estimator. Based on CQR method, we propose a weighted CQR (WCQR) method for singleindex models with heteroscedasticity and general error distributions. Because of the use of weights, the estimation bias is eliminated asymptotically. By comparing asymptotic relative efficiency, WCQR estimation outperforms the CQR estimation and least squares estimation. The simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods.

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