| 高维部分线性模型的变量选择和估计 |
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| 引用本文： | 杨宜平,薛留根.高维部分线性模型的变量选择和估计[J].应用概率统计,2011,27(2):172-182. |
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| 作者姓名： | 杨宜平 薛留根 |
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| 作者单位： | 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 |
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| 基金项目： | the National Natural Science Foundation of China，the Natural Science Foundation of Beijing，Research Fund of Chongqing Technology and Business University |
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| 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.
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| 关 键 词： | 部分线性模型 变量选择 Dantzig选择 SCAD |
Variable Selection and Estimation in High-Dimensional Partially Linear Models |
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| YANG YIPING,XUE LIUGEN.Variable Selection and Estimation in High-Dimensional Partially Linear Models[J].Chinese Journal of Applied Probability and Statisties,2011,27(2):172-182. |
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| Authors: | YANG YIPING XUE LIUGEN |
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| Institution: | Yang Yiping(College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing,400067)Xue Liugen(College of Applied Sciences,Beijing University of Technology,Beijing,100124) |
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| Abstract: | 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 models. We use Dantzig selector, applied to the linear part and various derivatives of nonpararnetric 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. |
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| Keywords: | Partially linear model variable selection Dantzig selector SCAD |
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