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高阶空间自回归模型的选择与平均估计

廖军,文丽,尹建鑫   

  1. 中国人民大学统计学院, 北京  100872
  • 出版日期:2021-05-25 发布日期:2021-08-12

廖军, 文丽, 尹建鑫. 高阶空间自回归模型的选择与平均估计[J]. 系统科学与数学, 2021, 41(5): 1400-1417.

LIAO Jun , WEN Li , YIN Jianxin. Model Selection and Averaging for  Higher-Order Spatial Autoregressive Model[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(5): 1400-1417.

Model Selection and Averaging for  Higher-Order Spatial Autoregressive Model

LIAO Jun ,WEN Li ,YIN Jianxin   

  1. School of Statistics, Renmin University of China, Beijing 100872
  • Online:2021-05-25 Published:2021-08-12
文章研究了高阶空间自回归模型的模型选择方法, 该方法可以同时进行空间权重矩阵和协变量的选择. 模型选择方法在Kullback-Leibler 损失意义下的渐近有效性得到证明. 此外, 文章进一步提出了高阶空间自回归模型的模型平均方法, 并证明了其渐近最优性. 数值模拟结果展示了模型选择方法的价值, 也表明了模型平均具有进一步提升模型选择效果的优势.
A model selection method for the higher-order spatial autoregressive model is studied in this paper, which can select the spatial weight matrix and covariate simultaneously. The asymptotic efficiency of model selection is proved in the sense of Kullback-Leibler loss. Further, we propose a model averaging method for the higher-order spatial autoregressive model, and its asymptotic optimality is established. The numerical simulation results demonstrate the merits of the model selection method and also show that the model averaging method can further improve the performance of model selection.
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