ADMM for High-Dimensional Sparse Penalized Quantile Regression. Issue 3 (3rd July 2018)

• Record Type: Journal Article
• Authors: Gu, Yuwen; Fan, Jun; Kong, Lingchen; Ma, Shiqian; Zou, Hui
• Is Part Of: Technometrics. Volume 60:Issue 3(2018)
• Page Start: 319
• Page End: 331
• Publication Date: 2018-07-03
• Subjects: Alternating direction method of multipliers -- Lasso -- Nonconvex penalty -- Quantile regression -- Variable selection; Statistical physics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; Engineering -- Statistical methods -- Periodicals; 519.5
• DOI: 10.1080/00401706.2017.1345703
• Languages: English
• ISSNs: 0040-1706

Abstract

ABSTRACT: Sparse penalized quantile regression is a useful tool for variable selection, robust estimation, and heteroscedasticity detection in high-dimensional data analysis. The computational issue of the sparse penalized quantile regression has not yet been fully resolved in the literature, due to nonsmoothness of the quantile regression loss function. We introduce fast alternating direction method of multipliers (ADMM) algorithms for computing the sparse penalized quantile regression. The convergence properties of the proposed algorithms are established. Numerical examples demonstrate the competitive performance of our algorithm: it significantly outperforms several other fast solvers for high-dimensional penalized quantile regression. Supplementary materials for this article are available online.