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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (2): 294-310.doi: 10.3969/j.issn.1005-3085.2024.02.007

• • 上一篇    下一篇

部分线性空间自回归模型的惩罚最小二乘方法

程瑶瑶,  李体政   

  1. 西安建筑科技大学理学院，西安 710055
  • 收稿日期:2021-05-25 接受日期:2021-08-20 出版日期:2024-04-15 发布日期:2024-06-15
  • 通讯作者: 李体政 E-mail: tizhengli@xauat.edu.cn
  • 基金资助:
    国家自然科学基金(11972273)；全国统计科学一般项目(2019LY36)；陕西省自然科学基金(2021JM349).

Penalized Least Squares Method of Partially Linear Spatial Autoregressive Model

CHENG Yaoyao,  LI Tizheng   

  1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055
  • Received:2021-05-25 Accepted:2021-08-20 Online:2024-04-15 Published:2024-06-15
  • Contact: T. Li. E-mail address: tizhengli@xauat.edu.cn}
  • Supported by:
    The National Natural Science Foundation of China (11972273); the National Statistical Science Project (2019LY36); the Natural Science Foundation of Shaanxi Province (2021JM349).

摘要：

部分线性空间自回归模型因具有参数空间自回归模型的解释能力和非参数空间自回归模型的灵活性而成为一类备受关注的半参数空间自回归模型。主要研究部分线性空间自回归模型的变量选择问题，基于轮廓拟最大似然方法和一类非凸罚函数，提出了一类惩罚最小二乘方法同时选择该模型的参数部分中重要解释变量和估计相应的非零回归系数。在适当的正则条件下，推导了回归系数的惩罚估计的收敛速度，并证明了所提出的变量选择方法具有Oracle性质。模拟研究和实际数据分析均表明所提出的变量选择方法具有满意的有限样本性质。

关键词: 空间相关, 部分线性空间自回归模型, 轮廓拟最大似然方法, 非凸罚函数

Abstract:

Partially linear spatial autoregressive model has attracted extensive attention in recent years because it combines explanatory power of parametric spatial autoregressive models and flexibility of nonparametric spatial autoregressive model. This paper considers the problem of variable selection in the partially linear spatial autoregressive model. Based on profile quasi-maximum likelihood method and a class of non-convex penalty function, a class of penalized least squares method is proposed to simultaneously select significant explanatory variables in parametric component of the model and estimate corresponding nonzero regression coefficients. Under appropriate regularity conditions, the rate of convergence of the penalized estimator of the regression coefficient vector is derived and it shows that the proposed variable selection method enjoys oracle property. Both simulation studies and real data analysis indicate that the proposed variable selection method has satisfactory finite sample performance.

Key words: spatial dependence, partially linear spatial autoregressive model, profile quasi-maximum likelihood method, non-convex penalty

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