Combining least-squares and quantile regressions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

5 Scopus Citations
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Original languageEnglish
Pages (from-to)3814-3828
Journal / PublicationJournal of Statistical Planning and Inference
Issue number12
Publication statusPublished - Dec 2011


Least-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. © 2011 Elsevier B.V.

Research Area(s)

  • Empirical likelihood, Estimating equations, Generalized method of moments, Kernel, Smoothing