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Hierarchically penalized quantile regression with multiple responses

Authors
Kang, JongkyeongShin, Seung JunPark, JaeshinBang, Sungwan
Issue Date
12월-2018
Publisher
KOREAN STATISTICAL SOC
Keywords
Multivariate response; Quantile regression; Regularization; Hierarchical penalty; Oracle property; Variable selection
Citation
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, v.47, no.4, pp.471 - 481
Indexed
SCIE
SCOPUS
KCI
Journal Title
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume
47
Number
4
Start Page
471
End Page
481
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/71267
DOI
10.1016/j.jkss.2018.05.004
ISSN
1226-3192
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. (C) 2018 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
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