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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 ›› 2026, Vol. 42 ›› Issue (6): 1029-1046.doi: 10.3969/j.issn.1005-3085.2025.06.004cstr: 32411.14.cjem.CN61-1269/O1.2025.06.004

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约束条件和异方差下部分线性空间自回归模型的统计推断

李体政,   谭允迪,   程瑶瑶   

  1. 西安建筑科技大学理学院，西安 710055
  • 收稿日期:2023-02-06 接受日期:2023-07-30 出版日期:2025-12-15 发布日期:2026-02-15
  • 基金资助:
    国家自然科学基金 (52170172; 11972273)；陕西省自然科学基金 (2024JC-YBMS-059)；陕西数理基础科学研究项目 (23JSY041).

Statistical Inference of Partially Linear Spatial Autoregressive Model under Constraint Conditions#br# and Heteroscedasticity#br#

LI Tizheng,   TAN Yundi,  CHENG Yaoyao   

  1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055
  • Received:2023-02-06 Accepted:2023-07-30 Online:2025-12-15 Published:2026-02-15
  • Supported by:
    The National Natural Science Foundation of China (52170172;11972273); the Natural Science Foundation of Shaanxi Province (2024JC-YBMS-059); the Shaanxi Fundamental Science Research Project for Mathematics and Physics (23JSY041).

摘要：

在回归分析的许多应用中，回归系数往往满足约束条件并且误差项不满足等方差假定，在约束条件和异方差下研究部分线性空间自回归模型的统计推断问题，基于局部多项式光滑方法、广义矩方法以及拉格朗日乘子方法，构建了模型参数和未知函数的约束估计，并在适当的正则条件下研究了所得估计的渐近性质。进一步，构造了一个Wald型统计量检验回归系数是否满足线性约束条件，并在零假设和备择假设下证明了检验统计量都渐近服从卡方分布。模拟研究和实例分析展示了所提出的估计和检验方法在有限样本时的表现。

关键词: 空间相关, 部分线性空间自回归模型, 约束条件, 异方差, 工具变量

Abstract:

In many applications of regression analysis, regression coefficients usually satisfy constraint conditions and error terms are heteroscedastic. This paper considers statistical inference of partially linear spatial autoregressive model with constraint conditions and heteroscedasticity. The constrained estimators of unknown parameters and function are established by combining local polynomial smoothing method, generalized method of moments and Lagrange multiplier method, and their asymptotic properties are investigated under appropriate regularity conditions. Furthermore, a Wald test statistic is constructed to test appropriateness of a linear constraint condition on the regression coefficients. It is shown that the proposed test statistic asymptotically follows Chi-squared distribution under both null and alternative hypotheses. Simulation studies and real data analysis are conducted to demonstrate finite sample property of the proposed estimation and testing methods.

Key words: spatial correlation, partially linear spatial autoregressive model, constraint conditions, heteroscedasticity, instrumental variables

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