Shrinkage estimation for identification of linear components in composite quantile additive models

Abstract

In this paper, we consider a new robust identification of linear parts in additive models. A one-step sparse algorithm based on local linear approximation is used for minimizing the proposed composite quantile regression (CQR) objective function. Under some mild conditions, the theoretical properties of the proposed CQR method are obtained. We also present some simulation studies and real data analysis to show the performance of the proposed procedure.

Keywords:

• Additive model
• Composite quantile regression
• Partially linear additive model
• Spline approximation
• Local linear approximation

Acknowledgments

Liu’s work is supported by the National Natural Science Foundation of China (Grant No. 11761020), China Postdoctoral Science Foundation(Grant No. 2017M623067), Science and Technology Foundation of Guizhou Province (Grant Nos. QKH20177222, QKH20183001), Scientific Research Foundation for Young Talents of Department of Education of Guizhou Province(Grant No. 2017104), Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant No. 2017BDKFJJ030). Ma’s work is supported by the Scientific Research Foundation for Young Talents of Department of Education of Guizhou Province (Grant No. 2016125), Science and Technology Foundation of Guizhou Province (Grant No. QKH20175788). Peng’s work is supported by the National Natural Science Foundation of China (Grant No. 61662009).

Additional information

Funding

Liu’s work is supported by the National Natural Science Foundation of China (Grant No. 11761020), China Postdoctoral Science Foundation(Grant No. 2017M623067), Science and Technology Foundation of Guizhou Province (Grant Nos. QKH20177222, QKH20183001), Scientific Research Foundation for Young Talents of Department of Education of Guizhou Province(Grant No. 2017104), Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant No. 2017BDKFJJ030). Ma’s work is supported by the Scientific Research Foundation for Young Talents of Department of Education of Guizhou Province (Grant No. 2016125), Science and Technology Foundation of Guizhou Province (Grant No. QKH20175788). Peng’s work is supported by the National Natural Science Foundation of China (Grant No. 61662009)