多元稳健估计抗差性分析
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摘要
介绍了鲁棒估计的原理,并在实例中使用MATLAB进行编程和比较,比较最小二乘法和鲁棒估计法得到的结果。结果显示:在多元数据变化趋于平稳(各个变量间之差不超过20%)并存在粗差的情况下,稳健估计能准确地剔除粗差,使回归方程更加准确,并获得更加准确的预测方程。而多元数据变化幅度比较大(各个变量间之差大于20%)时,稳健估计方法得到的结果与最小二乘方法基本一致。
The theory of robust estimation is introduced and MATLAB program is used to program in the example.The results obtain from the two methods of least squares and robust are compared.The results show that the robust estimation can eliminate the gross error accurately and make the regression equation more accurate and getting more accurate prediction equation when the variation of multivariate data tends to be stable(The difference between variables is less than 20%)and have gross error.However,the effect of robust estimation is same as the least-square method if the variation of multivariate data tends to be disorder(The difference between variables is more than 20%).
The theory of robust estimation is introduced and MATLAB program is used to program in the example.The results obtain from the two methods of least squares and robust are compared.The results show that the robust estimation can eliminate the gross error accurately and make the regression equation more accurate and getting more accurate prediction equation when the variation of multivariate data tends to be stable(The difference between variables is less than 20%)and have gross error.However,the effect of robust estimation is same as the least-square method if the variation of multivariate data tends to be disorder(The difference between variables is more than 20%).
引文
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[6]钟红,魏淑英.基于丹麦法稳健估计在地铁变形监测中的应用[J].吉林地质.2014,33(03):110-112.
[7]陈西强,黄张裕.抗差估计的选权迭代法分析与比较[J].测绘工程.2010,19(04):8-11.
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[2]刘佳丽,赵自雨,张永彬.稳健估计抗差性分析与应用[J].华北理工大学学报(自然科学版),2017,39(01):1-5.
[3]杨坤,简汉佳.基于稳健估计的GPS水准在线状工程中的应用[J].测绘通报,2014(10):57-59.
[4]陈永星.稳健估计在水准网数据处理中的应用[J].长春工程学院学报:自然科学版.2012,13(04):66-68.
[5]龚循强,李通,陈西江.总体最小二乘法在曲线拟合中的应用[J].地矿测绘.2012,28(03):4-6.
[6]钟红,魏淑英.基于丹麦法稳健估计在地铁变形监测中的应用[J].吉林地质.2014,33(03):110-112.
[7]陈西强,黄张裕.抗差估计的选权迭代法分析与比较[J].测绘工程.2010,19(04):8-11.
[8]吴杰,余腾.稳健估计及其在秩亏网中的应用[J].南京工程学院学报:自然科学版.2010,8(02):63-67.
[9]云磊.牛顿迭代法的MATLAB实现[J].信息通信,2011,(06):20-22.
[10]吕喜明,李明远.最小二乘曲线拟合的MATLAB实现[J].内蒙古民族大学学报:自然科学版.2009,24(02):125-127.
[11]彭仪普,伍绍浩,张莹超.基于稳健估计的沉降预测方法[J].铁道科学与工程学报.2014,11(05):112-117.