超高维纵向数据部分线性模型的特征筛选  

Feature Screening for Partially Linear Models With Ultrahigh-dimensional Longitudinal Data

作　　者：郭望 杨孝光 周鹏飞 李运明 Guo Wang;Yang Xiaoguang;Zhou Pengfei;Li Yunming(College of Mathematics,Southwest Jiaotong University,Chengdu 611756,China;Department of Information,Medical Support Center,The General Hospital of Western Theater Command,Chengdu 610083,China)

机构地区：[1]西南交通大学数学学院,成都611756 [2]西部战区总医院医疗保障中心信息科,成都610083

出　　处：《统计与决策》2024年第12期46-51,共6页Statistics & Decision

基　　金：全军保健专项科研课题(21BJZ39);西部战区总医院军事医学科研课题(2019ZY10,2021-XZYG-A14);中央高校基础研究培育支持计划项目(2682021ZTPY018)。

摘　　要：超高维纵向数据的特征筛选是超高维特征筛选的难点之一,其难点是在保证边际筛选快速的前提下估计工作相关系数矩阵。文章在部分线性模型的假定下,考虑到纵向数据组间独立、组内相关的特点,采用样本协方差去估计未知的工作协方差矩阵,提出了剖面有协方差阵的确定独立筛选(PMSIS)方法,并在一定正则条件下,证明了该方法具有确定筛选性质。通过蒙特卡洛数值模拟与肠道菌群实例数据验证了该方法的有限样本性质,结果表明,新提出的PMSIS方法能有效筛选弱相关的协变量。Feature screening of ultrahigh-dimensional longitudinal data is one of the difficulties of ultrahigh-dimensional feature screening,and the difficulty is to estimate the working correlation coefficient matrix under the premise of ensuring the speed of marginal screening.Under the assumption of partial linear model,this paper takes into account the characteristics of longitudinal data of between-group independence and within-group correlation,and uses sample covariance to estimate the unknown working covariance matrix,proposing a sure independent screening method with profile covariance matrix(PMSIS).The paper also theoretically proves that the method has the sure screening property under certain regularity conditions,and verifies the finite sample properties of the method through Monte Carlo numerical simulation and gut microbiota data.The results show that the new PMSIS method can be used to effectively screen weakly correlated covariates.

关 键 词：超高维 纵向数据 部分线性模型 特征筛选 确定筛选性质 

分 类 号：O212[理学—概率论与数理统计]