含内生变量的高维部分线性模型特征筛选
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国家社会科学基金资助项目(18BTJ035);重庆市自然科学基金资助面上项目(cstc2020jcyj-msxmX0006)


Feature Selection of High-Dimensional Partial Linear Models with Endogenous Covariates
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    摘要:

    主要研究了含有内生性协变量的超高维部分线性模型的重要特征筛选和变量选择问题。首先,为了消除数据内生性对特征筛选带来的选择性偏差,结合内生性协变量与工具变量的相关结构,给出了一个区分重要协变量和不重要协变量的充分条件,进而提出一种衡量变量边际效用的特征筛选方法。其次,利用提出的特征筛选方法,并结合剖面估计思想和两阶段正则估计方法,提出了一种识别重要协变量的变量选择方法。最后,在一定正则条件下,理论证明了所提出的变量选择方法可以消除数据内生性对变量选择带来的影响,从而保证了对协变量重要性具有排序一致性。

    Abstract:

    This study is mainly focused on the important feature selection and variable selection of ultra-high dimensional partial linear models with endogenous covariates. Firstly, in view of an elimination of the selective deviation of data endogeneity on feature selection, combined with the correlation structure of endogenous covariates and instrumental variables, a sufficient condition has thus been given to distinguish important covariates from unimportant covariates, followed by a proposed feature selection method to measure the marginal utility of variables. Secondly, a variable selection method is adopted for the identification of important covariates by using the proposed feature screening method, with a combination of the profile estimation idea and the two-stage regular estimation method. Finally, under certain regular conditions, the theory proves that the proposed variable selection method helps to eliminate the influence of data endogeneity on variable selection, thus ensuring the consistency of ranking the importance of covariates.

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陈海燕,赵培信.含内生变量的高维部分线性模型特征筛选[J].湖南工业大学学报,2023,37(1):83-90.

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  • 收稿日期:2022-03-19
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  • 在线发布日期: 2023-01-03
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