Hierarchically penalized quantile regression with multiple responses

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

doi:10.1016/j.jkss.2018.05.004

Hierarchically penalized quantile regression with multiple responses

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

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	471-481
Number of pages	11
Journal	Journal of the Korean Statistical Society
Volume	47
Issue number	4
DOIs	https://doi.org/10.1016/j.jkss.2018.05.004
Publication status	Published - 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

Keywords

Hierarchical penalty
Multivariate response
Oracle property
Quantile regression
Regularization
Variable selection

ASJC Scopus subject areas

Statistics and Probability

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10.1016/j.jkss.2018.05.004

Cite this

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abstract = "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.",

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AU - Shin, Seung Jun

AU - Park, Jaeshin

AU - Bang, Sungwan

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N2 - 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.

AB - 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.

KW - Hierarchical penalty

KW - Multivariate response

KW - Oracle property

KW - Quantile regression

KW - Regularization

KW - Variable selection

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JF - Journal of the Korean Statistical Society

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ER -

Hierarchically penalized quantile regression with multiple responses

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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