交叉熵方法理论上的缺陷及其改进研究——基于社会核算矩阵平衡和更新的分析

The Analysis and Improvement of Cross Entropy Approach

本文针对传统交叉熵(CE)方法在平衡和更新社会核算矩阵(SAM)研究中存在的缺陷进行分析,提出基于离差熵绝对值期望最小化的改进模型1和基于离差熵平方期望最小化的改进模型2。理论结果表明,传统的CE方法得到的解是本文所提出的基于离差熵绝对值期望最小化改进模型1的一种特殊情况。同时为检验模型改进前后的实际效果,本文运用蒙特卡罗方法进行模拟,得出改进后的模型2得到的SAM流量矩阵精度比传统的CE方法得到的精度更高,而改进后的模型1得到的精度却相对较低。

Focus on the defects of traditional Cross Entropy （CE） approach which applied for the balance and update of Social Accounting Matrix （SAM）, This paper proposes the Model Ⅰ which based on minimizing the expectation absolute value of the deviation entropy and Model Ⅱ which based on minimizing the expectation of the deviation entropy square. The theoretical results show that, the analytical solution solved by the traditional CE approach is a special case of model Ⅰ Meanwhile, this paper provides the Monte Carlo performance of both traditional CE approach and the improvemental ModelⅠ and Ⅱ. The simulation results show that, the traffic matrix of SAM for Model Ⅱ has higher accuracy than that for the traditional CE approach, but Model Ⅰ displays lower accuracy than the traditional CE approach.