基于面板数据的灰色点集关联分析模型  

Grey point set association analysis model based on panel data

作　　者：翟艳丽 罗格格 ZHAI Yan-li;LUO Ge-ge(School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,郑州450046

出　　处：《控制与决策》2024年第8期2801-2809,共9页Control and Decision

基　　金：河南省高等学校重点科研项目(18A630032).

摘　　要：针对面板数据样本行为矩阵间的关联性分析,从接近性视角提出基于面板数据的灰色点集关联分析模型.首先,将样本行为矩阵的二元指标子矩阵投射为空间中的点集,利用对应点的高度差建立对应点集的绝对离差矩阵,依据此矩阵中数据的平均值和标准差分别建立对应点集的绝对离差平均值关联系数和绝对离差标准差关联系数,基于此,构建灰色点集关联分析模型;然后,讨论模型的规范性、接近性、正定性、对称性等性质,对比分析发现,模型不仅不受指标排序的影响,且能够感知样本行为矩阵间数据差距的变化并有效反映其接近性;最后,利用灰色点集关联分析模型对豫中4个城市的空气质量进行定量评价,并基于此进行豫中4个城市的关联聚类,将豫中划分为3类污染区域,以期为豫中大气污染联防联控的区域划分提供理论支持.Aiming at the correlation analysis between the sample behavior matrices of panel data,a gray point set correlation analysis model based on panel data is proposed from the perspective of proximity.First,the binary index submatrix of the sample behavior matrix is projected into the point set in space,and the absolute deviation matrix of the corresponding point set is established by using the height difference of the corresponding point.Based on the average value and standard deviation of the data in this matrix,the correlation coefficients of the absolute deviation mean value and absolute deviation standard deviation of the corresponding point set are established respectively.Based on this,the grey point set association analysis model is constructed.Then,the properties of the model such as normalization,proximity,positive definiteness,and symmetry are discussed.Comparative analysis shows that the model is not only unaffected by index ranking,but also can perceive the changes of data gaps between sample behavior matrices and effectively reflect their proximity.Finally,the grey point set correlation analysis model is used to quantitatively evaluate the air quality of four cities in central Henan,and based on this,the correlation clustering of four cities in central Henan is carried out,dividing them into three types of pollution areas,in order to provide theoretical support for the regional division of air pollution joint prevention and control in central Henan.

关 键 词：面板数据 接近性关联度 点集 绝对离差 平均值 标准差 

分 类 号：N941.5[自然科学总论—系统科学]