CAJ | 학술논문

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。
일반선성회귀모형도가설예측변량불함오차,소유모형오차균집중우향응변량차복종정태분포,이허다실제응용중적변량병불부합저사가설,여유적문제난이명학예측변량화향응변량,관측양본집수도오염이함유리군치。당가설수도파배시,득도적고계삼수왕왕불능진실반영변량간적선성관계,도치모형불가용。위재가설수도파배시야능득도정학적모형,제출이방차선성EV모형적T-형회귀고계모형,이용최대사연고계원리,급출료T-형회귀고계삼수표체식화구해방법。최후장모형여방법래학정면파진급여지진구관계공식,병여기타방법비교검험,취득료교호적결과,대우연구해지구역사지진구석방고계구유중요적과학의의。본문급출적모형화방법환가이재지진지질、재해학등등영역득도응용,즉용우변량간통계관계식적학정,여b치적은건고계등。
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.