Efficient quantile regression for heteroscedastic models

Yoonsuh Jung, Yoonkyung Lee, Steven N. MacEachern

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Quantile 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.

Original languageEnglish
Pages (from-to)2548-2568
Number of pages21
JournalJournal of Statistical Computation and Simulation
Issue number13
Publication statusPublished - 2015 Sept 2
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported by the National Science Foundation [grant number DMS-1209194].

Publisher Copyright:
© 2014 Taylor & Francis.


  • check loss function
  • heteroscedasticity
  • quantile regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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