Jung, YoonsuhLee, YoonkyungMacEachern, Steven N.Lee, J2015-06-082014-11-012015-06-082015Jung, Y., Lee, Y., & MacEachern, S. N. (2015). Efficient quantile regression for heteroscedastic models. Journal of Statistical Computation and Simulation, 85(13), 2548–2568. http://doi.org/10.1080/00949655.2014.9672440094-9655https://hdl.handle.net/10289/9355Quantile regression (QR) provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. [Regularization of case-specific parameters for robustness and efficiency. Statist Sci. 2012;27(3):350–372] proposed efficient QR by rounding the sharp corner of the loss. The main modification generally involves an asymmetric ℓ₂ adjustment of the loss function around zero. We extend the idea of ℓ₂ adjusted QR to linear heterogeneous models. The ℓ₂ adjustment is constructed to diminish as sample size grows. Conditions to retain consistency properties are also provided.application/pdfThis is an author’s accepted version of an article published in the journal: Journal of Statistical Computation and Simulation. © 2015 Taylor & Francis.check loss functionheteroscedasticityquantile regressionJournal Article10.1080/00949655.2014.967244