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Interquantile shrinkage and variable selection in quantile regression

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  • Jiang, Liewen
  • Bondell, Howard D.
  • Wang, Huixia Judy

Abstract

Examination of multiple conditional quantile functions provides a comprehensive view of the relationship between the response and covariates. In situations where quantile slope coefficients share some common features, estimation efficiency and model interpretability can be improved by utilizing such commonality across quantiles. Furthermore, elimination of irrelevant predictors will also aid in estimation and interpretation. These motivations lead to the development of two penalization methods, which can identify the interquantile commonality and nonzero quantile coefficients simultaneously. The developed methods are based on a fused penalty that encourages sparsity of both quantile coefficients and interquantile slope differences. The oracle properties of the proposed penalization methods are established. Through numerical investigations, it is demonstrated that the proposed methods lead to simpler model structure and higher estimation efficiency than the traditional quantile regression estimation.

Suggested Citation

  • Jiang, Liewen & Bondell, Howard D. & Wang, Huixia Judy, 2014. "Interquantile shrinkage and variable selection in quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 208-219.
    • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:208-219
    DOI: 10.1016/j.csda.2013.08.006
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    3. He, Qianchuan & Kong, Linglong & Wang, Yanhua & Wang, Sijian & Chan, Timothy A. & Holland, Eric, 2016. "Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 222-239.
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    6. Muhammad Amin & Lixin Song & Milton Abdul Thorlie & Xiaoguang Wang, 2015. "SCAD-penalized quantile regression for high-dimensional data analysis and variable selection," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 212-235, August.

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