杨鑫, 李冰月, 田萍. 超高维部分线性模型的PRAR变量选择[J]. 应用概率统计, 2021, 37(6): 551-568. DOI: 10.3969/j.issn.1001-4268.2021.06.001
引用本文: 杨鑫, 李冰月, 田萍. 超高维部分线性模型的PRAR变量选择[J]. 应用概率统计, 2021, 37(6): 551-568. DOI: 10.3969/j.issn.1001-4268.2021.06.001
YANG Xin, LI Bingyue, TIAN Ping. partially linear model; variable selection;high-dimensional data; Lasso; sign consistency; regularization afterretention[J]. Chinese Journal of Applied Probability and Statistics, 2021, 37(6): 551-568. DOI: 10.3969/j.issn.1001-4268.2021.06.001
Citation: YANG Xin, LI Bingyue, TIAN Ping. partially linear model; variable selection;high-dimensional data; Lasso; sign consistency; regularization afterretention[J]. Chinese Journal of Applied Probability and Statistics, 2021, 37(6): 551-568. DOI: 10.3969/j.issn.1001-4268.2021.06.001

超高维部分线性模型的PRAR变量选择

partially linear model; variable selection;high-dimensional data; Lasso; sign consistency; regularization afterretention

  • 摘要: 本文考虑超高维部分线性模型,其中参数向量维数是样本量的指数阶.基于profile最小二乘方法和保留正则化方法,本文提出了新的变量选择方法用来解决超高维部分线性模型的变量选择问题.在一定的正则条件下, 证明了所得估计量的符号相合性. 通过数值模拟和实例分析,将该方法与Lasso、SIS-Lasso、自适应Lasso方法进行对比,发现所提方法在恢复线性部分参数向量符号方面明显优于其它方法.

     

    Abstract: In this paper, we consider the ultrahigh dimensional partially linear model, in which the dimension of the parametric vector is exponential order of the sample size. Based on profile least squares and regularization after retention method, we propose a new method to perform variable selection for the ultrahigh dimensional partially linear model. Under certain regularity conditions, it is proved that the estimator achieves sign consistency. Compared with Lasso, SIS-Lasso and adaptive Lasso, it is found that the proposed method is better in terms of recovering the coefficient sign of linear part through the numerical simulation and real data analysis.

     

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