General composite quantile regression: Theory and methods |
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Authors: | Yanke Wu Maozai Tian |
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Institution: | 1. School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, China;2. Center for Applied Statistics, School of Statistics Renmin University of China, Beijing, China;3. Center for Applied Statistics, School of Statistics Renmin University of China, Beijing, China;4. School of Statistics and Information, Xinjiang University of Finance and Economics, Xinjiang, China;5. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou, Gansu, China |
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Abstract: | AbstractIn 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. |
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Keywords: | Asymptotic relative efficiency general composite quantile regression oracle property weight function |
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