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

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.

Keywords:

• Ultra-high dimensional model
• longitudinal data
• quantile regression
• variable selection

MSC 2010 subject classifications:

• 62J05
• 62J99

Notes

1 URL for:http://data.stats.gov.cn/easyquery.htm?cn=C01.

Additional information

Funding

This work was supported by the National Social Science Foundation of China under Grant 16BTJ015.