Penalized expectile regression: an alternative to penalized quantile regression

Lina Liao, Cheolwoo Park, Hosik Choi

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


This paper concerns the study of the entire conditional distribution of a response given predictors in a heterogeneous regression setting. A common approach to address heterogeneous data is quantile regression, which utilizes the minimization of the L 1 norm. As an alternative to quantile regression, we consider expectile regression, which relies on the minimization of the asymmetric L 2 norm and detects heteroscedasticity effectively. We assume that only a small set of predictors is relevant to the response and develop penalized expectile regression with SCAD and adaptive LASSO penalties. With properly chosen tuning parameters, we show that the proposed estimators display oracle properties. A numerical study using simulated and real examples demonstrates the competitive performance of the proposed penalized expectile regression, and its combined use with penalized quantile regression would be helpful and recommended for practitioners.

Original languageEnglish
Pages (from-to)409-438
Number of pages30
JournalAnnals of the Institute of Statistical Mathematics
Issue number2
StatePublished - 1 Apr 2019


  • Asymptotics
  • Expectile regression
  • Heteroscedasticity
  • Penalized regression
  • Variable selection


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