基于弹性网惩罚的高维部分线性模型的稳健变量选择

Robust Variable Selection Based on High-Dimensional Partial Linear Model of Elastic Net Penalty

摘要: 高维数据下部分线性模型的变量选择方法大多基于最小二乘回归估计展开，但随着数据复杂性的提升，极端、异常等因素使得以往模型的估计效率直线下滑。为此，本文基于弹性网络法与分位数回归相结合的正则化理论，提出了一种应对高维数据下部分线性模型的稳健变量选择模型。该模型不仅可以有效处理强相关变量组的数据，还可以在面对离群点或存在异方差时仍达到较好的稳健性。此外，理论上证明了在一定条件下模型估计量的相合性和稀疏性，最后通过数值模拟，与其他变量选择方法作比较，进一步表明了该方法的优越性。

Abstract: Most of the variable selection methods of some linear models under high-dimensional data are based on least squares regression estimation, but with the increase of data complexity, extreme and abnormal factors make the estimation efficiency of previous model plummet. Therefore, based on the regularization theory combining elastic network method and quantile regression, this paper proposes a robust variable selection model to cope with some linear models under high-dimensional data. The model can not only effectively handle data for groups of strongly cor-related variables, but also achieve better robustness in the face of outliers or heteroscedasticity. In addition, the coherence and sparsity of model estimators under certain conditions are theoretically proved, and finally the superiority of this method is further demonstrated by numerical simulation and comparison with other variable selection methods.