Article ID Journal Published Year Pages File Type
1148407 Journal of Statistical Planning and Inference 2016 21 Pages PDF
Abstract

•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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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