一种基于投影的多响应特征筛选方法  

A Projection-Based Feature Screening Method for Multiple Responses

作　　者：邹丰 崔恒建 Feng Zou;Hengjian Cui(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,P.R.China;School of Mathematical Sciences,Capital Normal University,Beijing 100048,P.R.China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073 [2]首都师范大学数学科学学院,北京100048

出　　处：《数学学报(中文版)》2025年第1期1-29,共29页Acta Mathematica Sinica:Chinese Series

基　　金：国家自然科学基金项目(12031016,11971324);国家自然科学基金项目(12201317);国家资助博士后研究人员计划C档(批准号:GZC20233143);中南财经政法大学中央高校基本科研业务费专项资金资助(编号:2722024BQ065)。

摘　　要：本文提出了一种非负投影相关系数(non-negative projection correlation coefficient(NPCC))来度量两个随机向量之间的相关性,其中投影方向来自标准多元正态分布.NPCC是非负的且当且仅当两个随机向量独立时,其取值为0.此外,它的样本估计不涉及调节参数,也不需要对随机向量施加任何矩条件.基于NPCC,我们进一步提出了一种适用于超高维数据的特征筛选程序.该程序具有稳健性、与模型无关且在弱假设下同时享有确定筛选性质和秩相合性.蒙特卡罗模拟研究表明,与现有方法相比,基于NPCC的筛选程序具有很好的竞争力.最后,我们将所提出的筛选程序应用于实际数据分析.In this paper,a nonnegative projection correlation coefficient(NPCC)is proposed to measure the dependence between two random vectors,where the projection direction comes from the standard multivariate normal distribution.The NPCC is nonnegative and is zero if and only if the two random vectors are independent.Also,its estimation is free of tuning parameters and does not require any moment conditions on the random vectors.Based on the NPCC,we further propose a novel feature screening procedure for ultrahigh dimensional data,which is robust,model-free and enjoys both sure screening and rank consistency properties under weak assumptions.Monte Carlo simulation studies indicate that the NPCC-based screening procedure have strong competitive advantages over the existing methods.Lastly,we also use a real data example to illustrate the application of the proposed procedure.

关 键 词：投影相关系数 相关性度量 确定筛选性质 秩相合 

分 类 号：O212[理学—概率论与数理统计]