基于稀疏超高维非参数可加模型的条件独立筛选  

Conditional Independence Screening in Sparse Ultra-high Dimensional Nonparametric Additive Models

作　　者：徐萍 钟思敏 李斌斌 熊文俊 XU Ping;ZHONG Simin;LI Binbin;XIONG Wenjun(School of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《广西师范大学学报（自然科学版）》2022年第1期100-107,共8页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11801102,11861017);广西高等学校千名中青年骨干教师培育计划资助项目。

摘　　要：变量筛选是处理超高维数据的一种有效方法。针对部分变量与响应变量显著相关,Barut等基于线性模型假定提出CSIS方法,能有效降低伪变量错选概率。但CSIS方法线性模型假定严苛,实际研究中有时不能事先确定模型结构。由此,本文基于非参数可加模型提出条件非参数独立筛选方法(CNIS),不需要对模型结构进行假定,增大了适用范围。同时,在适当条件下,证明本文方法第1阶段的筛选具有一致性筛选性质,能以概率1保留重要变量;第2阶段的变量选择也具有良好相合性。Monte Carlo数据模拟结果表明:相较于NIS方法,本文方法表现更好。Variable screening is an effective method for processing ultra-high-dimensional data.Barut et al.considered that some of the known variables are significantly related to the response variables,and propose the CSIS method based on the assumption of a linear model.This method can effectively reduce the probability of false variable selection.However,its linear model assumptions are more stringent.In actual research,the structure of the model cannot be determined in advance.Therefore,this paper proposes a conditional non-parametric independent screening method(CNIS)based on a non-parametric additive model,which does not need to make assumptions about the model structure,to increases the scope of application.At the same time,under appropriate conditions,it is proved that the screening in the first stage of the method has consistent screening properties and can retain important variables with probability 1.The variable selection in the second stage also has good consistency.The simulation results based on Monte Carlo data show that this method has better performance than the NIS method.

关 键 词：变量筛选 可加模型 变量选择 确定筛选 

分 类 号：O212[理学—概率论与数理统计]