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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

• • 上一篇    

部分线性变系数空间自回归模型的惩罚轮廓拟最大似然方法

李体政,  方  可   

  1. 西安建筑科技大学理学院，西安 710055
  • 收稿日期:2021-07-23 接受日期:2022-08-01
  • 基金资助:
    国家自然科学基金 (11972273; 52170172)；陕西省自然科学基金 (2024JC-YBMS-059)；全国统计科学一般项目 (2019LY36)；陕西数理基础科学研究项目 (23JSY041).

Penalized Profile Quasi-maximum Likelihood Method of Partially Linear Varying Coefficient Spatial Autoregressive Model

LI Tizheng,  FANG Ke   

  1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055
  • Received:2021-07-23 Accepted:2022-08-01
  • Supported by:
    The National Natural Science Foundation of China (11972273; 52170172); the Natural Science Foundation of Shaanxi Province (2024JC-YBMS-059); the National Statistical Science Project (2019LY36); the Shaanxi Fundamental Science Research Project for Mathematics and Physics (23JSY041).

摘要：

主要研究了部分线性变系数空间自回归模型的变量选择问题。结合拟最大似然方法、局部线性光滑方法以及一类非凸罚函数，提出了一个变量选择方法用于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零参数。大量模拟研究表明，所提出的变量选择方法具有满意的有限样本性质，并且关于空间权矩阵的稀疏度、空间相关强度、系数函数的复杂度以及误差分布的非正态性非常稳健。特别地，当样本容量较大且罚函数选择合适时，即使解释变量的相关性较强或者模型中含有较多不重要解释变量，所提出的变量选择方法仍然具有比较满意的有限样本性质。通过分析波士顿房屋价格数据考察了所提出的变量选择方法的实际应用效果。

关键词: 空间相关, 部分线性变系数空间自回归模型, 拟最大似然方法, 局部线性光滑方法, 惩罚似然方法

Abstract:

The problem of variable selection is considered in partially linear varying coefficient spatial autoregressive model. By combining profile quasi-maximum likelihood method and a class of non-convex penalty function, a variable selection method is proposed to simultaneously select important explanatory variables in parametric component of the partially linear varying coefficient spatial autoregressive model and estimate the corresponding nonzero parameters. Extensive simulation studies show that the proposed variable selection method is of satisfactory finite sample performance. Especially, the proposed variable selection method is quite robust to degree of sparseness of spatial weight matrix, intensity of spatial dependence, degree of complexity of coefficient function and non-normality of error distribution, and even works well in the case where correlation among explanatory variables is strong or number of unimportant explanatory variables is large provided that appropriate penalty function is used and sample size is moderately large. As an illustrative example, the proposed variable selection method is applied to analyze the popular Boston housing price data.

Key words: spatial dependence, partially linear varying coefficient spatial autoregressive model, quasi-maximum likelihood method, local linear smoothing method, penalized likelihood method

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