离散GM(1,1)参数估计的3种方法比较
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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。
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).
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).
引文
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[10]胡攀.离散DGM(1,1,tα)模型[J].数学的实践与认识,2016,46(5):222-230HU P.Discrete GM(1,1,tα)Model[J].Mathematics in Practice and Theory,2016,46(5):222-230(in Chinese)
[2]郑照宁,武玉英,包涵龄.GM模型的病态性问题[J].中国管理科学,2001,9(5):38-44ZHENG Z N,WU Y Y,BAO H L.Morbidity Problem in Grey Model[J].Chinese Journal of Management Science,2001,9(5):39-45(in Chinese)
[3]何文章,宋国乡.估计GM(1,1)模型中参数的一族算法[J].系统工程理论与实践,2005,25(1):69-75HE W Z,SONG G X.A Class of Algorithms for Estimating GM(1,1)Model Parameter[J].Systems Engineering Theory&Practice,2005,25(1):69-75(in Chinese)
[4]何霞,刘卫锋.一种优化GM(1,1)模型及其应用[J].重庆工商大学学报(自然科学版),2011,28(3):254-257HE X,LIU W F.An Optimized GM(1,1)Model and Its Application[J].Journal of Chongqing Technology and Business University(Natural Science Edition),2011,28(3):254-257(in Chinese)
[5]何霞.灰色GM(1,1)模型参数估计的加权最小二乘方法[J].运筹与管理,2012,21(6):23-27HE X.Weighted Least Squares for Estimating Parameters of Grey GM(1,1)Model[J].Operation and Management,2012,21(6):23-27(in Chinese)
[6]仇环,曲国庆,苏晓庆.GM(1,1)模型的改进[J].山东理工大学学报(自然科学版),2008(2):5-8QIU H,QU G Q,SU X Q.The Improvement of the GM(1,1)Model[J].Journal of Shandong University of Technology(Natural Science Edition),2008(2):5-8(in Chinese)
[7]李洪然,张阿根,叶为民.参数累积估计灰色模型及地面沉降预测[J].岩土力学,2008,29(12):3417-3421LI H R,ZHANG A G,YE W M.Accumulating Method GM(1,1)Model and Prediction of Land Subsidence[J].Rock and Soil Mechanics,2008,29(12):3417-3421(in Chinese)
[8]曾祥艳,肖新平.累积法GM(1,1)模型的改进与应用[J].统计与决策,2009(5):32-35ZENG X Y,XIAO X P.An Accumulating Method GM(1,1)Model and Its Application[J].Statistics and Decision,2009(5):32-35(in Chinese)
[9]郭文艳,任大卫.新息改进GM(1,1)模型参数估计的新方法[J].计算机工程与应用,2008,44(24):62-64GUO W Y,REN D W.New Method of Estimating Model Parameters of Modified GM(1,1)[J].Computer Engineering and Applications,2008,44(24):62-64(in Chinese)
[10]胡攀.离散DGM(1,1,tα)模型[J].数学的实践与认识,2016,46(5):222-230HU P.Discrete GM(1,1,tα)Model[J].Mathematics in Practice and Theory,2016,46(5):222-230(in Chinese)