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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (9): 35-48.doi: 10.6040/j.issn.1671-9352.0.2025.200

• • 上一篇    

部分线性可加高阶空间自回归模型的SCAD-L2惩罚变量选择

黄实1,程素丽1,2*,郭盛亮1   

  1. 1.重庆工商大学数学与统计学院, 重庆 400067;2.重庆工商大学统计智能计算与监测重庆市重点实验室, 重庆 400067
  • 发布日期:2026-09-30
  • 通讯作者: 程素丽(1984— ),女,副教授,博士,研究方向为空间统计. E-mail:chengsuli@ctbu.edu.cn
  • 作者简介:黄实(1999— ),男,硕士研究生,研究方向为半参数统计和空间统计. E-mail:huangshi2979@163.com*通信作者:程素丽(1984— ),女,副教授,博士,研究方向为空间统计. E-mail:chengsuli@ctbu.edu.cn
  • 基金资助:
    教育部人文社会科学基金资助项目(23YJC910001);重庆市自然科学基金资助项目(CSTB2022NSCQ-MSX0300);重庆市教委科学技术研究项目(KJQN202200831)

Variable selection of SCAD-L2 penalty for the partially linear additive higher-order spatial autoregressive model

HUANG Shi1, CHENG Suli1,2*, GUO Shengliang1   

  1. 1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
    2. Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, Chongqing Technology and Business University, Chongqing 400067, China
  • Published:2026-09-30

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摘要： 提出关于部分线性可加高阶空间自回归模型的SCAD-L2惩罚最小二乘方法,能够同时对高阶空间滞后项和线性解释变量进行组变量选择和参数估计。证明所提出的变量选择方法具有稀疏性和渐近正态性。蒙特卡罗数值模拟进一步验证SCAD-L2方法在小样本中的优良性质,最终将所提方法应用于波士顿房价数据集分析,结果显示平均房间数和处于较低地位人口所占比例对波士顿房价影响较大。

关键词: 变量选择, 可加模型, 空间自回归模型, 分组效应

Abstract: A SCAD-L2 penalized least squares method for partially linear additive higher-order spatial autoregressive models is proposed, which can simultaneously perform group variable selection and parameter estimation for higher-order spatial lag terms and linear explanatory variables. It is proved that the proposed variable selection method possesses sparseness and asymptotic normality. The Monte Carlo numerical simulation further confirmed the excellent properties of the SCAD-L2 method in small samples. Finally, the proposed approach is applied to the analysis of the Boston housing price dataset, and the results show that the average number of rooms and the proportion of lower-status population have a significant impact on Boston housing price.

Key words: variable selection, additive model, spatial autoregressive model, grouping effect

中图分类号: 

  • O212
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