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Sparsity identification in ultra-high dimensional quantile regression models with longitudinal data

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  • Xianli Gao
  • Qiang Liu

Abstract

In this paper, we propose a variable selection method for quantile regression model in ultra-high dimensional longitudinal data called as the weighted adaptive robust lasso (WAR-Lasso) which is double-robustness. We derive the consistency and the model selection oracle property of WAR-Lasso. Simulation studies show the double-robustness of WAR-Lasso in both cases of heavy-tailed distribution of the errors and the heavy contaminations of the covariates. WAR-Lasso outperform other methods such as SCAD and etc. A real data analysis is carried out. It shows that WAR-Lasso tends to select fewer variables and the estimated coefficients are in line with economic significance.

Suggested Citation

  • Xianli Gao & Qiang Liu, 2020. "Sparsity identification in ultra-high dimensional quantile regression models with longitudinal data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(19), pages 4712-4736, October.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:19:p:4712-4736
    DOI: 10.1080/03610926.2019.1604966
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