正交最小二乘法在确定台站震级偏差校正公式中的应用
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摘要
经典最小二乘回归模型假设自变量没有误差而所有误差都集中于响应变量,但是许多应用领域中实际问题的自变量含有噪声数据,往往不符合这个假设,经典最小二乘回归模型不再适用。为克服这一缺陷,介绍了正交最小二乘回归模型和参数估计算法。对经典最小二乘和正交最小二乘回归系数进行了理论分析和计算机数值仿真,结果表明当自变量和响应变量都含有误差时,正交最小二乘法优于经典最小二乘法。最后将经典最小二乘法和正交最小二乘法用于蒙城地震台2001~2006年地震数据,确定了台站震级偏差校正公式,并对它们的结果进行了详细比较。
The classical least square regression model assume that the independent variables are measured exactly and all the errors are focused on the response variables.However,in many real problems in certain areas,some of the independent variables are contaminated with errors;the classical least square regression model can't deal with this problem.To overcome this drawback,the orthogonal least square regression model is introduced.The comparisons between orthogonal least square regression and classical least square regression are done through theory analysis and computer simulation.Our results validate that when independent and independent variables are corrupted by noise,the estimation obtained with the orthogonal least square regression are superior to those with the classical least square regression.At last,the orthogonal least square regression is employed to earthquake catalogues of Mengcheng seismic station from 2001 to 2006,the results obtained by the above two methods are compared in detail.
The classical least square regression model assume that the independent variables are measured exactly and all the errors are focused on the response variables.However,in many real problems in certain areas,some of the independent variables are contaminated with errors;the classical least square regression model can't deal with this problem.To overcome this drawback,the orthogonal least square regression model is introduced.The comparisons between orthogonal least square regression and classical least square regression are done through theory analysis and computer simulation.Our results validate that when independent and independent variables are corrupted by noise,the estimation obtained with the orthogonal least square regression are superior to those with the classical least square regression.At last,the orthogonal least square regression is employed to earthquake catalogues of Mengcheng seismic station from 2001 to 2006,the results obtained by the above two methods are compared in detail.
引文
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[3]刘瑞丰,陈运泰,Peter Bormann,等.中国地震台网与美国地震台网测定震级的对比(Ⅱ)——面波震级[J].地震学报,2006,28(1):1-7.
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[9]曾献军,陈俊,张娟.FBS-3观测系统与仿真地方震震级偏差分析[J].防灾科技学院学报,2008,10(1):25-29.
[2]刘瑞丰,陈运泰,Peter Bormann,等.中国地震台网与美国地震台网测定震级的对比(Ⅰ)——体波震级[J].地震学报,2005,27(6):583-587.
[3]刘瑞丰,陈运泰,Peter Bormann,等.中国地震台网与美国地震台网测定震级的对比(Ⅱ)——面波震级[J].地震学报,2006,28(1):1-7.
[4]Huffel V S,Markovsky I,Vaccaro J R,et al.Total Least Squares and Errors-in-Variables Modeling[J].IEEE Trans.SignalProcessing,2007,87(10):228 1-228 2.
[5]Markovsky I,Huffel V S.Overview of total least-squares methods[J].IEEE Trans.Signal Processing,2007,87(10):228 3-230 2.
[6]程龙生.基于errors-in-variables的预测模型及其应用[J].数理统计与管理,2005,24(2):55-59.
[7]盛骤,谢式千,潘承毅.概率论与数理统计(第四版)[M].北京:高等教育出版社,2008:244-255.
[8]Jackson J D,Dunlevy J A.Orthogonal Least Squares and the Interchangeability of Alternative Proxy Variables in the Social Sci-ences[J].The Statistician,1988,37(1):7-14.
[9]曾献军,陈俊,张娟.FBS-3观测系统与仿真地方震震级偏差分析[J].防灾科技学院学报,2008,10(1):25-29.
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