Modified check loss for efficient estimation via model selection in quantile regression

Yoonsuh Jung, Steven N. MacEachern, Hang Joon Kim

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The check loss function is used to define quantile regression. In cross-validation, it is also employed as a validation function when the true distribution is unknown. However, our empirical study indicates that validation with the check loss often leads to overfitting the data. In this work, we suggest a modified or L2-adjusted check loss which rounds the sharp corner in the middle of check loss. This has the effect of guarding against overfitting to some extent. The adjustment is devised to shrink to zero as sample size grows. Through various simulation settings of linear and nonlinear regressions, the improvement due to modification of the check loss by quadratic adjustment is examined empirically.

Original languageEnglish
Pages (from-to)866-886
Number of pages21
JournalJournal of Applied Statistics
Issue number5
Publication statusPublished - 2021

Bibliographical note

Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.


  • Check loss
  • cross-validation
  • quantile regression
  • quantile regression spline
  • quantile smoothing spline

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Modified check loss for efficient estimation via model selection in quantile regression'. Together they form a unique fingerprint.

Cite this