基于面板数据的灰色向量模关联模型及其应用  

Grey vector modulus incidence model based on panel data and itsapplication

作　　者：党耀国[1] 王一博 王俊杰[1] 杨绍闻 DANG Yao-guo;WANG Yi-bo;WANG Jun-jie;YANG Shao-wen(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]南京航空航天大学经济与管理学院,南京210016

出　　处：《控制与决策》2024年第10期3451-3458,共8页Control and Decision

基　　金：国家自然基金项目(72001107,72271120);中国博士后科学基金项目(2020T130297,2019M660119)。

摘　　要：针对现有面板数据灰色关联模型中不同几何特征的可比性问题,以及关联序受对象排列顺序影响的问题,从时间维和对象维两个方面构建基于面板数据的灰色向量模关联模型.首先,以向量的形式对面板数据进行表征,进而定义指标多维度上的绝对变化量和相对变化量两种几何特征向量,并基于特征向量对各几何特征进行相应的无量纲化处理;然后,在时间维度考虑指标的横向发展绝对量和相对量向量的模得到时间维灰色向量模关联度,在对象维度考虑指标的纵向振荡绝对量和相对量向量的模得到对象维灰色向量模关联度,对两维度加权平均得到面板数据的灰色向量模关联度;其次,对面板数据灰色向量模关联模型的性质如规范性、接近性、数乘变换保序性等进行讨论,验证模型的实用性和有效性,且模型不受对象排列顺序的影响;最后,利用所提出的模型对江苏省地区大气污染问题进行研究,以期为江苏省大气污染防治工作提供理论支持.Aiming at the comparability problem of different geometric features in the existing panel data grey incidence model,and the problem that the incidence order is affected by the order of objects,a grey vector modulus incidence model based on panel data is constructed.Firstly,the panel data is characterized in the form of vectors,and then two geometric feature vectors of absolute change and relative change in multi-dimension of the index are defined,and the corresponding dimensionless processing of each geometric feature is carried out based on the feature vector.Then,the time dimension grey vector modulus incidence degree is obtained by considering the modulus of the horizontal development absolute quantity and the relative quantity.The object dimension grey vector modulus incidence degree is obtained by considering the modulus of the vertical oscillation absolute quantity and the relative quantity.The grey vector modulus incidence degree of the panel data is obtained by two dimensions.The properties of the grey vector norm incidence model of panel data are discussed.Finally,the proposed model is used to study the air pollution problem in Jiangsu Province.

关 键 词：灰色系统 灰色关联分析 面板数据 向量模 大气污染 

分 类 号：N941.5[自然科学总论—系统科学]