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Hierarchically penalized quantile regression

Authors
Kang, JongkyeongBang, SungwanJhun, Myoungshic
Issue Date
22-1월-2016
Publisher
TAYLOR & FRANCIS LTD
Keywords
group variable selection; hierarchical regularization; linear programming; quantile regression
Citation
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, v.86, no.2, pp.340 - 356
Indexed
SCIE
SCOPUS
Journal Title
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
Volume
86
Number
2
Start Page
340
End Page
356
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/89768
DOI
10.1080/00949655.2015.1014038
ISSN
0094-9655
Abstract
In many regression problems, predictors are naturally grouped. For example, when a set of dummy variables is used to represent categorical variables, or a set of basis functions of continuous variables is included in the predictor set, it is important to carry out a feature selection both at the group level and at individual variable levels within the group simultaneously. To incorporate the group and variables within-group information into a regularized model fitting, several regularization methods have been developed, including the Cox regression and the conditional mean regression. Complementary to earlier works, the simultaneous group and within-group variables selection method is examined in quantile regression. We propose a hierarchically penalized quantile regression, and show that the hierarchical penalty possesses the oracle property in quantile regression, as well as in the Cox regression. The proposed method is evaluated through simulation studies and a real data application.
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