高维部分线性模型的变量选择和估计(英文)  

Variable Selection and Estimation in High-DimensionalPartially Linear Models

作　　者：杨宜平[1] 薛留根[2] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]北京工业大学应用数理学院,北京100124

出　　处：《应用概率统计》2011年第2期172-182,共11页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation of China(10871013,10871217);the NaturalScience Foundation of Beijing(1072004);Research Fund of Chongqing Technology and Business University(20105609)

摘　　要：考虑高维部分线性模型,提出了同时进行变量选择和估计兴趣参数的变量选择方法.将Dantzig变量选择应用到线性部分及非参数部分的各阶导数,从而获得参数和非参数部分的估计,且参数部分的估计具有稀疏性,证明了估计的非渐近理论界.最后,模拟研究了有限样本的性质.In this paper, we propose an approach for achieving simultaneously variable selection and estimation for the linear and nonparametric components in high-dimensional＂ partially linear mod- els. We use Dantzig selector, applied to the linear part and various derivatives of nonparametric component, to achieve sparsity in the linear part and produce nonparametric estimators. Non- asymptotic theoretical bounds on the estimator error are obtained. The finite sample properties of the proposed approach are investigated through a simulation study.

关 键 词：部分线性模型 变量选择 Dantzig选择 SCAD 

分 类 号：O212.7[理学—概率论与数理统计]