基于熵权法的小样本灰色置信区间估计

摘要

In order to solve the problem of small samples data of gray estimation and grey interval estima-tion, the sample average error and sample error standard deviation were introduced into the grey distance measure, and the existing grey estimation algorithm was improved. In the process of intensive expansion of small samples data, the gray degree of the estimation could be improved. Based on the distribution of the data itself, the gray distance matrix of data was designed, and the weight of grey point estimation was proposed . Finally the small samples data of parameter estimation was tested to examing the simulation re-sults. The results highlighted the effectiveness of the proposed algorithm, and verified the correctness of the theoretical analysis .%针对小样本数据的灰色点估计和灰色区间估计问题，将样本误差均值、样本误差标准差引入到灰色距离测度中，改进了已有灰色估计算法。在对小样本数据进行密集扩充过程中，可以提高灰色估计的区分度。该算法利用数据本身分布特点，设计了数据间的灰色距离矩阵，提出了基于熵权法的灰色点估计权重计算方法。最后结合小样本数据进行了参数估计的仿真实例验证，在对小样本数据进行Bootstrap重抽样法作用下进行了不同灰色点估计和区间估计的比较，突出了所提算法的有效性，验证了理论分析结果的正确性。