Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and between groups is essential. However, existing quantile regression methods often fail to meet this dual objective. To address this gap, we introduce the adaptive sparse group lasso penalized quantile regression, which integrates adaptive lasso and adaptive group lasso penalties. We optimize the model parameters via the alternating direction method of multipliers (ADMM) applied to the dual problem, and establish global convergence. Through extensive simulation studies and real data analyses, we demonstrate (i) the efficacy of the proposed method in achieving simultaneous within- and between-group sparsity, and (ii) the computational efficiency of our algorithm relative to existing alternatives.

翻译：稀疏惩罚分位数回归为高维数据分析中的变量选择与稳健估计提供了有效框架。当解释变量以分组形式组织时，实现组内与组间双重稀疏性至关重要。然而现有分位数回归方法往往难以满足这一双重目标。为弥补该不足，我们提出自适应稀疏组Lasso惩罚分位数回归模型，该模型融合了自适应Lasso与自适应组Lasso惩罚项。通过将交替方向乘子法（ADMM）应用于对偶问题实现模型参数优化，并建立了全局收敛性理论。大量模拟实验与真实数据分析表明：（i）该方法能有效实现组内与组间同步稀疏化；（ii）相较于现有替代方法，本算法具有计算效率优势。