基于惩罚最小绝对偏差的部分线性空间自回归模型的稳健变量选择  

Robust Variable Selection of Partial linear Spatial Autoregressive Model Based on Penalty Minimum Absolute Deviation

作　　者：赵培信[1,2] 张杰文 ZHAO Peixin;ZHANG Jiewen(School of Mathematics and Statistics of Chongqing Technology and Business University,Chongqing 400067,China;Chongqing Key Laboratory of Social Economic and Applied Statistics,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]重庆工商大学经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《四川文理学院学报》2023年第2期7-16,共10页Sichuan University of Arts and Science Journal

基　　金：国家社会科学基金一般项目(18BTJ035);重庆市自然科学基金面上项目(cstc2020jcyj-msxmX0006)。

摘　　要：结合B样条逼近以及工具变量调整技术,并利用惩罚最小绝对偏差方法,对部分线性空间自回归模型提出了一种稳健变量选择方法.理论上证明了所提出的变量选择方法可以相合地识别出模型中的重要协变量和不重要协变量,并给出了所得正则估计的收敛速度.所提出的变量选择过程对模型中的参数分量和非参数分量的估计可以一步同时完成,避免了非参数分量的估计对参数分量变量选择的影响,因此具有较好的稳健性和有效性.Combined with B-spline approximation and instrumental variable adjustment technology,and used the pe-nalized least absolute deviations method,a robust variable selection method for partial linear spatial autoregressive model is proposed.It was proved theoretically that the proposed variable selection method can identify the important covariates and unimportant covariates in the model,and the convergence rate of the obtained canonical estimation is given.The pro-posed variable selection process can estimate the parametric and nonparametric components in the model at the same time,avoiding the influence of nonparametric components on variable selection,so it has good robustness and effective-ness.

关 键 词：惩罚最小绝对偏差 部分线性空间自回归模型 稳健估计 工具变量 B样条基函数 

分 类 号：O212.7[理学—概率论与数理统计]