Incorporating graphical structure of predictors in sparse quantile regression
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Officially Accepted for Publication


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AbstractQuantile regression in high dimensional settings is useful in analyzing high dimensional heterogeneous data. In this paper, different from existing methods in quantile regression which treat all the predictors equally with the same priori, we take advantage of the graphical structure among predictors to improve the performance of parameter estimation, model selection and prediction in sparse quantile regression. It is shown under mild conditions that the proposed method enjoys the model selection consistency and the oracle properties. An alternating direction method of multipliers (ADMM) algorithm with a linearization technique is proposed to implement the proposed method numerically, and its convergence is justified. Simulation studies are conducted, showing that the proposed method is superior to existing methods in terms of estimation accuracy and predictive power. The proposed method is also applied to a real dataset.
Acceptance Date10/02/2020
All Author(s) ListZhanfeng Wang, Xianhui Liu, Wenlu Tang, Yuanyuan Lin
Journal nameJournal of Business and Economic Statistics
Detailed descriptionThe article is officially accepted on Feb 10, 2020.
Year2020
Place of PublicationUSA
ISSN0735-0015
eISSN1537-2707
LanguagesEnglish-United States
KeywordsQuantile regression, sparse regression, ADMM algorithm, graphical structure

Last updated on 2020-23-10 at 00:21