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Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization

Authors
Bang, SungwanJhun, Myoungshic
Issue Date
1-4월-2012
Publisher
ELSEVIER
Keywords
Factor selection; Linear programming; Quantile regression; Regularization; Sup-norm
Citation
COMPUTATIONAL STATISTICS & DATA ANALYSIS, v.56, no.4, pp.813 - 826
Indexed
SCIE
SCOPUS
Journal Title
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume
56
Number
4
Start Page
813
End Page
826
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/108755
DOI
10.1016/j.csda.2011.01.026
ISSN
0167-9473
Abstract
Some regularization methods, including the group lasso and the adaptive group lasso, have been developed for the automatic selection of grouped variables (factors) in conditional mean regression. In many practical situations, such a problem arises naturally when a set of dummy variables is used to represent a categorical factor and/or when a set of basis functions of a continuous variable is included in the predictor set. Complementary to these earlier works, the simultaneous and automatic factor selection is examined in quantile regression. To incorporate the factor information into regularized model fitting, the adaptive sup-norm regularized quantile regression is proposed, which penalizes the empirical check loss function by the sum of factor-wise adaptive sup-norm penalties. It is shown that the proposed method possesses the oracle property. A simulation study demonstrates that the proposed method is a more appropriate tool for factor selection than the adaptive lasso regularized quantile regression. (C) 2011 Elsevier B.V. All rights reserved.
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