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Combining least-squares and quantile regressions
Zhou, Yong2,3; Wan, Alan T. K.1; Yuan, Yuan3
AbstractLeast-squares and quantile regressions are method of moments techniques that are typically used in isolation. A leading example where efficiency may be gained by combining least-squares and quantile regressions is one where some information on the error quantiles is available but the error distribution cannot be fully specified. This estimation problem may be cast in terms of solving an over-determined estimating equation (EE) system for which the generalized method of moments (GMM) and empirical likelihood (EL) are approaches of recognized importance. The major difficulty with implementing these techniques here is that the EEs associated with the quantiles are non-differentiable. In this paper, we develop a kernel-based smoothing technique for non-smooth EEs, and derive the asymptotic properties of the GMM and maximum smoothed EL (MSEL) estimators based on the smoothed EEs. Via a simulation study, we investigate the finite sample properties of the GMM and MSEL estimators that combine least-squares and quantile moment relationships. Applications to real datasets are also considered. (C) 2011 Elsevier B.V. All rights reserved.
KeywordEmpirical likelihood Estimating equations Generalized method of moments Kernel Smoothing
Funding ProjectNational Natural Science Funds for Distinguished Young Scholar[70825004] ; National Natural Science Foundation of China (NSFC)[10628104] ; National Natural Science Foundation of China (NSFC)[10731010] ; National Basic Research Program[2007CB814902] ; Creative Research Groups of China[10721101] ; Hong Kong Research Grants Council[CityU-102709] ; City University of Hong Kong[CityU-7008126]
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000294149800015
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Document Type期刊论文
Corresponding AuthorWan, Alan T. K.
Affiliation1.City Univ Hong Kong, Dept Management Sci, Kowloon, Hong Kong, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
3.Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai 200433, Peoples R China
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GB/T 7714
Zhou, Yong,Wan, Alan T. K.,Yuan, Yuan. Combining least-squares and quantile regressions[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE,2011,141(12):3814-3828.
APA Zhou, Yong,Wan, Alan T. K.,&Yuan, Yuan.(2011).Combining least-squares and quantile regressions.JOURNAL OF STATISTICAL PLANNING AND INFERENCE,141(12),3814-3828.
MLA Zhou, Yong,et al."Combining least-squares and quantile regressions".JOURNAL OF STATISTICAL PLANNING AND INFERENCE 141.12(2011):3814-3828.
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