Abstract: In view of the shortcomings of the existing grey incidence theory, this paper puts forward the idea of characteristic test for grey incidence degree, and constructs the characteristic test method of matrix grey incidence degree. First, the matrix grey incidence model is optimized. The characteristic difference matrix is defined by the difference of behavior matrix, and the matrix 2 norm is used to construct the incidence degree formula. Then, the stability and trend of characteristic difference matrix are analyzed. The stability coefficient is constructed in the form of variation coefficient, and the trend coefficients are estimated by the least square method. These two coefficients together constitute the characteristic test method of matrix grey incidence degree. Finally, the model is applied to the chronic multidimensional poverty analysis of Enshi Prefecture in Hubei Province. Compared with the existing model, it is found that the evaluation results of correlation degree effectively distinguish the poverty situation of 8 cities and counties in Enshi Prefecture. The characteristic test method complements the results from two aspects of poverty uncertainty and trend. The feasibility and practicability of the model are verified.

Key words: grey incidence, behavior matrix, characteristic test, multidimensional poverty

摘要： 针对现有灰色关联理论的不足, 本文提出灰色关联的特征检验思路, 构建了矩阵型灰色关联度的特征检验方法。首先优化矩阵型灰色关联模型, 利用行为矩阵差值定义特征差异矩阵, 采用矩阵2范数构建关联度公式。而后分析特征差异矩阵的稳定性与趋势性, 利用变异系数形式构建稳定性系数, 利用最小二乘法估计趋势性系数, 两者共同组成矩阵型灰色关联度的特征检验方法。最后, 本文模型被应用于湖北省恩施州的长期多维贫困分析, 在与现有模型的比较中, 发现关联度评估结果有效区分了恩施州8个市县的贫困情况, 特征检验方法从贫困不确定性和趋势性两方面对结果进行补充, 验证了模型的可行性与实用性。

关键词: 灰色关联, 行为矩阵, 特征检验, 多维贫困