统计与决策2024，Vol.40Issue(9)：43-48,6.DOI:10.13546/j.cnki.tjyjc.2024.09.007
超高维数据下部分线性可加分位数回归模型的变量选择
Variable Selection for Partial Linear Additive Quantile Regression Model Under Ultra-high-dimensional Data
摘要
Abstract
In ultrahigh dimensional data,on the one hand,the dimensionality of covariates may be much larger than the sam-ple size,even growing exponentially with the sample size;on the other hand,ultrahigh dimensional data are typically heteroge-neous,where the influence of covariates on the center of the conditional distribution may differ greatly from their influence on the tails,leading to complex situations such as heavy tails and outliers.This paper investigates variable selection and robust estima-tion of partial linear additive quantile regression models under the condition of divergence of covariate dimension and ultrahigh di-mension.Firstly,in order to achieve model sparsity and nonparametric smoothness,a non-convex Atan double penalty is intro-duced,and the proposed optimization problem is solved by using a quantile iterative coordinate descent algorithm;the theoretical properties of the proposed double penalty estimator are demonstrated under the selection of appropriate regularization parameters.Subsequently,the performance of the proposed method is verified through simulation studies.The simulations results indicate that the proposed method outperforms other penalty methods,especially in the case of data with heavy tails.Finally,the practicality of the proposed method is verified through empirical analysis of blood sample data from cancer screening patients.关键词
超高维数据/分位数回归/部分线性可加/变量选择/Atan双惩罚Key words
ultrahigh dimensional data/quantile regression/partial linear additivity/variable selection/Atan double penalty分类
数理科学引用本文复制引用
白永昕,钱曼玲,田茂再..超高维数据下部分线性可加分位数回归模型的变量选择[J].统计与决策,2024,40(9):43-48,6.基金项目
北京市自然科学基金资助项目(1242005) （1242005）
北京信息科技大学校科研基金资助项目(2022XJJ31) （2022XJJ31）
