一种有效且稳健的变量选择方法  

An effective and robust variable selection method

作　　者：胡毓榆 郭子君 陈梦醒 樊亚莉[1] HU Yuyu;GUO Zijun;CHEN Mengxing;FAN Yali(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2023年第3期244-252,共9页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学青年基金资助项目(11401383)。

摘　　要：当数据中存在异常值时,一些基于最小二乘估计的统计模型会产生较大的偏差,最小一乘估计对异常值具有比较强的抵抗能力。考虑到数据中可能存在异常值的情况,用绝对值损失代替平方损失,针对同时具有变量稀疏性和相邻系数差分稀疏性这种结构的线性模型,提出了最小一乘融合熔断自适应岭估计模型(LAD-Fused-BAR)。该模型将上一步估计的回归系数倒数的平方作为下一步惩罚权重,自适应地给予不同变量不同的惩罚,通过不断迭代得到最终解。运用交替方向乘子法(ADMM)求解LAD-Fused-BAR模型,并证明了ADMM算法的收敛性。数值模拟和实证分析也验证了该模型的有效性和稳健性。Some statistical models based on least squares estimation will produce large bias when there are outliers in the data.The least absolute deviation has strong resistance to outliers.Considering the influence of the outliers in the data,the square loss was replaced with the absolute loss.Aiming at the linear model of a structure that has both variable sparsity and sparsity of adjacent coefficient differences,the least absolute deviation fused broken adaptive ridge estimation model(LAD-Fused-BAR)was proposed.The square of the reciprocal of the regression coefficient estimated in the previous step was taken as the penalty weight for the next step,different penalties were adaptively given to different variables,and the final solution was obtained through continuous iteration.The alternating direction multiplier method(ADMM)was adopted to solve the LAD-Fused-BAR model and prove the convergence of the ADMM algorithm.Additionally,numerical simulation and empirical analysis confirm the efficacy and robustness of the proposed methodology.

关 键 词：LAD-Fused-BAR模型 稳健回归 交替方向乘子法 

分 类 号：O212.1[理学—概率论与数理统计]