| 摘要: |
| 针对离散灰色模型GM(1,1)中参数估计方法及模型稳定性问题，选取3种估计参数的方法进行讨论——最小二乘法、最小一乘法和累积法;为了更好地比较不同估计方法的差异，统一赋以相同的初值，并以拟合误差、关联度和条件数作为评价指标，借助MATLAB软件对两类实例数据进行分析——递增序列和递减序列;实验结果表明:在误差方面，累积法优于最小一乘和最小二乘，在模型稳定性方面，累积法优于最小二乘法，总之，对于递增和递减序列数据，累积法估计GM(1,1)中参数最优。 |
| 关键词: 离散灰色模型 参数估计 模型稳定性 |
| DOI： |
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| Comparison of Three Methods for Discrete GM (1,1) Parameter Estimation |
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ZHANG Peng
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| Abstract: |
| Aiming at estimating parameter and model stability in the discrete GM(1,1), this paper discusses three methods: the least square method,the least absolute deviation and accumulating method. In order to compare the differences of different estimation methods, the same initial values are uniformly assigned. Taking fitting error, degree of relevance and conditional number as evaluating indicators, the paper uses the MATLAB software to analyze two kinds of instance data: increasing sequence and decreasing sequence. The results show that the accumulative method is better than the least absolute deviation and least square method in the aspect of error, and accumulation method is superior to least square method in the aspect of stability. In summary, the cumulative method is best to estimate parameters in GM (1,1). |
| Key words: discrete grey model parameter estimation model stability |
