大规模三模网络自回归模型

数学物理学报 ›› 2024, Vol. 44 ›› Issue (3): 783-803.

大规模三模网络自回归模型

卫奕冰,朱复康^*()

吉林大学数学学院长春 130012

收稿日期:2023-04-28 修回日期:2023-11-10 出版日期:2024-06-26 发布日期:2024-05-17
通讯作者: *朱复康，Email:zfk8010@163.com
基金资助:
国家自然科学基金(12271206);吉林省教育厅科学研究项目(JJKH20231122KJ)

Autoregressive Model for Large-scale Three-mode Networks

Wei Yibing,Zhu Fukang^*()

School of Mathematics, Jilin University, Changchun 130012

Received:2023-04-28 Revised:2023-11-10 Online:2024-06-26 Published:2024-05-17
Supported by:
NSFC(12271206);Science and Technology Research Planning Project of Jilin Provincial Department of Education(JJKH20231122KJ)

摘要/Abstract

摘要：

在双模网络自回归 (NAR) 模型的基础上给出了三模 NAR 模型. 该模型考虑了大规模社交网络中三种类型的节点, 且边只允许出现在不同类型的节点之间. 首先介绍了模型的定义以及模型的可逆性与参数可识别性, 考虑了拟极大似然和条件最小二乘估计方法及相应估计量的大样本性质. 其次, 在多种设定下进行了数值模拟, 对估计方法的准确性与计算效率进行了对比, 最后分析了一个实际例子.

关键词: 三模 NAR 模型, 拟极大似然, 条件最小二乘, 大样本性质

Abstract:

Based on the two-mode network autoregressive (NAR) model, the specific form of the three-mode NAR model is given. This model considers three types of nodes in large-scale social networks, and edges are only allowed to occur between different types of nodes. First, the definition of the model, the reversibility and parameter identification of the model are introduced, and the estimation methods of quasi-maximum likelihood and conditional least squares and the large sample properties of the corresponding estimators are considered. Second, numerical simulations are carried out in multiple cases, the accuracy of the estimation methods and computational efficiency are compared, and finally a practical example is analyzed.

Key words: Three-mode NAR model, Quasi-maximum likelihood, Conditional least squares, Large-sample properties

中图分类号:

O212

卫奕冰, 朱复康. 大规模三模网络自回归模型[J]. 数学物理学报, 2024, 44(3): 783-803.

Wei Yibing, Zhu Fukang. Autoregressive Model for Large-scale Three-mode Networks[J]. Acta mathematica scientia,Series A, 2024, 44(3): 783-803.

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