Hierarchically penalized quantile regression with multiple responses

Jongkyeong Kang, Seung Jun Shin, Jaeshin Park, Sungwan Bang

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We study variable selection in quantile regression with multiple responses. Instead of applying conventional penalized quantile regression to each response separately, it is desired to solve them simultaneously when the sparsity patterns of the regression coefficients for different responses are similar, which is often the case in practice. In this paper, we propose employing a hierarchical penalty that enables us to detect a common sparsity pattern shared between different responses as well as additional sparsity patterns within the selected variables. We establish the oracle property of the proposed method and demonstrate it offers better performance than existing approaches.

Original languageEnglish
Pages (from-to)471-481
Number of pages11
JournalJournal of the Korean Statistical Society
Issue number4
Publication statusPublished - 2018 Dec

Bibliographical note

Funding Information:
Bang was partially supported by National Research Foundation of Korea (NRF) Grant No. 2015R1C1A1A02036473 , and Shin was partially supported by National Research Foundation of Korea (NRF) Grant No. 2015R1C1A1A01054913 .

Publisher Copyright:
© 2018 The Korean Statistical Society


  • Hierarchical penalty
  • Multivariate response
  • Oracle property
  • Quantile regression
  • Regularization
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability


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