Composite quantile regression and variable selection in single-index coefficient model

• Proposing a composite minimizing average check loss estimation procedure for composite quantile regression in single-index coefficient model.
• Establishing the asymptotic normalities of the proposed estimator.
• Comparing the asymptotic relative efficiencies of the proposed estimators with those discussed by least square method.
• Investigating a variable selection procedure by combining the proposed estimation method with adaptive LASSO penalized method.
• Established the oracle property of the proposed variable selection method.

In this paper, we propose a composite minimizing average check loss estimation procedure for composite quantile regression (CQR) in the single-index coefficient model (SICM). The asymptotic normalities of the proposed estimators are established, and the asymptotic relative efficiencies (ARE) of the proposed estimators compared with those by least square method are also discussed. We further investigate a variable selection procedure by combining the proposed estimation method with adaptive LASSO penalized method in CQR of SICM. The oracle property of the proposed variable selection method is also established. Simulations with various non-normal errors and one real data application are conducted to assess the finite sample performance of the proposed estimation and variable selection methods.