一种自适应稀疏Group Lasso分位数回归估计

An Adaptive Sparse Group Lasso Quantile Regression Estimation

稀疏惩罚分位数回归是高维数据分析中进行变量选择和稳健估计的重要工具。对于具有分组解释变量的问题,期望达到组内和组间稀疏的理想效果,但是许多现有方法未能实现这一目标。文章将自适应Lasso和自适应Group Lasso相结合,构建了一种自适应稀疏Group Lasso惩罚分位数回归(Q-AdSGL)模型,给出了基于ADMM算法的模型求解方法,并讨论了估计量的Oracle性质。通过Monte Carlo模拟研究和实例分析证明了所提模型和算法的有效性。

Sparse penalized quantile regression is an important tool for variable selection and robust estimation in high-dimensional data analysis.For problems with grouped explanatory variables,the desired effect of sparsity within and between groups is expected,but many existing methods fail to achieve this goal.This paper constructs an adaptive sparse Group Lasso penalized quantile regression(Q-AdSGL)model that combines adaptive Lasso and adaptive Group Lasso,presents a model solving method based on ADMM algorithm,and also discusses the Oracle properties of estimators.Finally,the paper employs Monte Carlo simulation and case analysis to verify the effectiveness of the proposed model and algorithm.