广西师范大学学报（自然科学版） ›› 2024, Vol. 42 ›› Issue (4): 100-114.doi: 10.16088/j.issn.1001-6600.2023052501

• 研究论文 • 上一篇    下一篇

含空间自相关误差的空间自回归模型的调整经验似然推断

唐洁1, 秦永松1,2*   

  1. 1.广西师范大学 数学与统计学院, 广西 桂林 541006;
    2.广西多源信息挖掘与安全重点实验室(广西师范大学),广西 桂林 541004
  • 收稿日期:2023-05-25 修回日期:2023-07-29 出版日期:2024-07-25 发布日期:2024-09-05
  • 通讯作者: 秦永松(1964—), 男, 湖北鄂州人, 广西师范大学教授, 博导。E-mail:ysqin@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金(12061017,12161009); 广西多源信息挖掘与安全重点实验室系统性研究课题(22-A-01-01); 广西研究生教育创新计划项目(YJSCXP202104)

Adjusted Empirical Likelihood for Spatial Autoregressive Models with Spatial Autoregressive Disturbances

TANG Jie1, QIN Yongsong1,2*   

  1. 1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China;
    2. Guangxi Key Lab of Multi-source Information Mining & Security (Guangxi Normal University), Guilin Guangxi 541004, China
  • Received:2023-05-25 Revised:2023-07-29 Online:2024-07-25 Published:2024-09-05

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摘要： 本文研究含空间自相关误差的空间自回归模型的调整经验似然推断问题。利用调整经验似然方法,构造出含空间自相关误差的空间自回归模型的调整经验似然比统计量,证明调整经验似然统计量的极限分布为卡方分布,并模拟比较调整经验似然与一般经验似然方法的优劣。模拟结果表明:调整经验似然比一般经验似然置信域的覆盖精度更高,计算速度更快。在样本容量较大时,无论误差项是否服从正态分布,一般经验似然方法和调整经验似然方法均可;在样本容量较小时,推荐使用调整经验似然方法。

关键词: 空间自相关误差, 空间SARAR模型, 调整经验似然, 覆盖率

Abstract: The adjustment empirical likelihood inference of spatial autoregressive models with spatial autoregressive errors is studied in this paper. Using adjusted empirical likelihood method, an adjusted empirical likelihood ratio statistic is constructed for spatial autoregressive models with spatial autoregressive errors. It is shown that the limit distribution of the adjusted empirical likelihood statistic is a chi-squared distribution. The advantages and disadvantages of the adjusted empirical likelihood method are compared with the general empirical likelihood method through simulations. Simulation results show that the adjusted empirical likelihood region has higher coverage accuracy and is faster in implementation than that of the general empirical likelihood. When the sample size is large, both general empirical likelihood method and adjusted empirical likelihood method can be used whether the error term follows a normal distribution or not. But when the sample size is small, it is recommended to use the adjusted empirical likelihood method.

Key words: spatial autoregressive error, spatial ARAR model, adjusted empirical likelihood, confidence region

中图分类号:  O212.1

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