超高维数据边际经验似然独立筛选方法（英文）  

Marginal Empirical Likelihood Independence Screening in Sparse Ultrahigh Dimensional Additive Models

作　　者：张俊英[1,2] 张日权 王航[2] 陆智萍 ZHANG Junying;ZHANG Riquan;WANG Hang;LU Zhiping(School of Statistics, East China Normal University, Shanghai, 200062, China;Department of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China;Department of Mathematics, Shanxi Datong University, Datong, 037009, China)

机构地区：[1]华东师范大学统计学院,上海200062 [2]太原理工大学数学系,太原030024 [3]山西大同大学数学系,大同037009

出　　处：《应用概率统计》2019年第2期126-140,共15页Chinese Journal of Applied Probability and Statistics

基　　金：supported in part by the National Natural Science Foundation of China(Grant Nos.11171112;11201190);the Doctoral Fund of Ministry of Education of China(Grant No.20130076110004);the 111 Project of China(Grant No.B14019)

摘　　要：可加模型通过协变量函数对响应变量起作用,是更加灵活的非参统计模型.当协变量个数大于样本数且以指数阶增大时,将维数降到经典方法可解决的范围是统计学家急需解决的问题.本文研究了超高维数据可加模型的变量筛选问题,提出了边际经验似然变量筛选方法.该方法通过排列在0点的边际经验似然率选择变量.我们证明了选择变量集以概率1渐进包含真实变量集;提出了迭代边际经验似然变量筛选方法.数据模拟和实数据分析验证了所提方法的可行性.The additive model is a more flexible nonparametric statistical model which allows a data-analytic transform of the covariates. When the number of covariates is big and grows exponentially with the sample size the urgent issue is to reduce dimensionality from high to a moderate scale. In this paper, we propose and investigate marginal empirical likelihood screening methods in ultra-high dimensional additive models. The proposed nonparametric screening method selects variables by ranking a measure of the marginal empirical likelihood ratio evaluated at zero to differentiate contributions of each covariate given to a response variable. We show that, under some mild technical conditions, the proposed marginal empirical likelihood screening methods have a sure screening property and the extent to which the dimensionality can be reduced is also explicitly quantified. We also propose a data-driven thresholding and an iterative marginal empirical likelihood methods to enhance the finite sample performance for fitting sparse additive models.Simulation results and real data analysis demonstrate the proposed methods work competitively and performs better than competitive methods in error of a heteroscedastic case.

关 键 词：边际经验似然筛选 非参回归模型 变量选择 维数缩减 

分 类 号：O212.7[理学—概率论与数理统计]