异方差线性EV模型T-型估计在确定面波震级与地震矩关系式中的应用
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摘要
一般线性回归模型都假设预测变量不含误差,所有模型误差均集中于响应变量且服从正态分布,而许多实际应用中的变量并不符合这些假设,如有的问题难以明确预测变量和响应变量,观测样本集受到污染而含有离群值。当假设受到破坏时,得到的估计参数往往不能真实反映变量间的线性关系,导致模型不可用。为在假设受到破坏时也能得到正确的模型,提出异方差线性EV模型的T-型回归估计模型,利用最大似然估计原理,给出了T-型回归估计参数表达式和求解方法。最后将模型与方法来确定面波震级与地震矩关系公式,并与其他方法比较检验,取得了较好的结果,对于研究该地区历史地震矩释放估计具有重要的科学意义。本文给出的模型和方法还可以在地震地质、灾害学等等领域得到应用,即用于变量间统计关系式的确定,如b值的稳健估计等。
The general linear regression model assumes that the independent variables are measured exactly and that the only errors,which are normal distribution,are in the response to variables.However,many of the variables in practical application do not accord with these assumptions.For example,some prediction variables and response variables are difficult to clear in some problems,observation is contaminated with errors.If the assumption is damaged,because the estimated parameter can't always really reflect the linear relationship between variables,the model is not available.In order to get the right model when the assumption is damaged,we put forward heteroscedastic model of linear EV T-type regression estimation model.Then,using maximum likelihood estimation principle,this paper gives the T-type regression estimation parameter expression and the solving method.With the model and method to determine the surface wave magnitude and seismic moment relationship formula,in comparison with other methods,the model and method obtain good results.The study of the historical earthquakes in release has an important moment estimate scientific significance.The model and the method given in this paper can also be used in the earthquake geology,disaster areas,and so on.The model and the method are used to determine the statistic formula between variables,such as b value of the robust estimation,etc.
The general linear regression model assumes that the independent variables are measured exactly and that the only errors,which are normal distribution,are in the response to variables.However,many of the variables in practical application do not accord with these assumptions.For example,some prediction variables and response variables are difficult to clear in some problems,observation is contaminated with errors.If the assumption is damaged,because the estimated parameter can't always really reflect the linear relationship between variables,the model is not available.In order to get the right model when the assumption is damaged,we put forward heteroscedastic model of linear EV T-type regression estimation model.Then,using maximum likelihood estimation principle,this paper gives the T-type regression estimation parameter expression and the solving method.With the model and method to determine the surface wave magnitude and seismic moment relationship formula,in comparison with other methods,the model and method obtain good results.The study of the historical earthquakes in release has an important moment estimate scientific significance.The model and the method given in this paper can also be used in the earthquake geology,disaster areas,and so on.The model and the method are used to determine the statistic formula between variables,such as b value of the robust estimation,etc.
引文
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[10]曲延军,杨马陵.稳健估计b值及中强震异常特征研究[J].华南地震,2001,21(2):13-19.
[2]王福昌,曹慧荣,万永革.线性Errors-in-Variables模型在确定汶川地震主震断层面中的应用[J].数理统计与管理,2010,29(3):381-390.
[3]崔恒建.线性模型和线性EV模型中的T-型回归估计和EM算法[J].应用概率统计,2006,22(3):321-328.
[4]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.
[5]Lange K.L.,Little R.J.A.,Taylor J.M.G.Robust statistical modeling using the t distribution[J].Journal of the American Statistical Association,1989,84(408):881-896.
[6]Bolfarine H.,Arellano-Valle R.B.Robust modelling inmeasurement error models using the t distribution.Brazilian Journal of Probability and Statistics,1994,8(1):67-84.
[7]Cheng C.-L.,Riu J.On estimating linear relationships when both variables are subject to heteroscedastic measurement errors.Technometrics,2006,48(4):511-519.
[8]万永革,沈正康,甘卫军,等.华北地区大地震矩释放率和GPS应变率的一致性研究[J].中国地震,2005,21(1):33-40.
[9]盛骤,潘承毅,谢式千.概率论与数理统计[M].北京:高等教育出版社,2008:13-19.
[10]曲延军,杨马陵.稳健估计b值及中强震异常特征研究[J].华南地震,2001,21(2):13-19.
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