General composite quantile regression: Theory and methods

Abstract

In this article, we propose a new regression method called general composite quantile regression (GCQR) which releases the unrealistic finite error variance assumption being imposed by the traditional least squares (LS) method. Unlike the recently proposed composite quantile regression (CQR) method, our proposed GCQR allows any continuous non-uniform density/weight function. As a result, determination of the number of uniform quantile positions is not required. Most importantly, the proposed GCQR criterion can be readily transformed to a linear programing problem, which substantially reduces the computing time. Our theoretical and empirical results show that the GCQR is generally efficient than the CQR and LS if the weight function is appropriately chosen. The oracle properties of the penalized GCQR are also provided. Our simulation results are consistent with the derived theoretical findings. A real data example is analyzed to demonstrate our methodologies.

Keywords:

• Asymptotic relative efficiency
• general composite quantile regression
• oracle property
• weight function

Additional information

Funding

The work was partially supported by the National Natural Science Foundation of China (No. 11861042), the major research projects of philosophy and social science of the Chinese Ministry of Education (No. 15JZD015), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (No. 18XNL012), China Statistical Research Project (No. 2016LD03), the Fund of the Key Research Center of Humanities and Social Sciences in the general Colleges and Universities of Xinjiang Uygur Autonomous Region and The Project of Flying Apsaras Scholar of Lanzhou University of Finance & Economics. The work of M. L. Tang was partially supported by the Research Fund of the Project under the Faculty Development Scheme from the Research Grants Council of the Hong Kong Special Administrative Region, China (RGC Ref. No. UGC/FDS14/P01/16) and the National Natural Science Foundation of China (Grant No. 11871124).