A Study Of Heteroscedasticity Test And Estimation Method In Linear Regression Model

The classical linear regression model assumes that the random error terms have the same variance,however,in many practical situations the variances of the random perturbation terms of the model are not exactly equal,i.e.,the model has heteroskedasticity.In this case,using ordinary least squares to calculate the model parameters,the estimates obtained will not have validity,the significance test of the coefficients of the variables loses its meaning,and the prediction of the model will also lose its meaning.Therefore,it is very important to use a reasonable heteroskedasticity test to verify the existence of heteroskedasticity in the regression model and to estimate the covariance matrix of the parameter vector more accurately to make the hypothesis testing of the regression parameters more precise.First,the M-G-Q test is proposed in this paper.In the linear regression model,the G-Q test cannot be directly applied to the multivariate model,and many scholars have proposed improved G-Q tests so that they can be applied to the multivariate linear regression model,but these improved G-Q tests have the problems of cumbersome test steps and insufficient accuracy.In this paper,based on the idea of variable selection,the explanatory variable that has the greatest influence on the variance of the regression disturbance term is selected based on the significance test,and then the overall G-Q test is completed by sorting the sample observations by this explanatory variable from largest to smallest.The numerical simulation shows that the M-G-Q test is easier than the existing improved G-Q test,and the accuracy of the M-G-Q test is higher compared to other scholars’ improvements of the G-Q test.The feasibility of the M-G-Q test is also demonstrated by example analysis.Second,the HCCv estimation is proposed.Since White proved HC0 as the heteroskedasticity consistent covariance array estimator,many scholars have proposed improvements for its slow convergence and large sample requirement,and these methods are collectively called heteroskedasticity consistent covariance array estimators(HCCMEs),and the existing HCCMEs methods are HC0,HC1,HC2,HC3,HC4,HC5,HC4 m,HC5m,and HC6,all of which are consistent estimates of the parameter covaryance matrix.In this paper,based on the existing HCCMEs,a new estimator HCCv is proposed to address the problems of its poor applicability and accuracy.The new estimator is more accurate in a variety of heteroskedasticity cases,and the paper proves the conclusion through a large number of simulation experiments and verifies its feasibility by example analysis.Finally,the innovations and shortcomings of the whole paper are summarized,and the future research directions are prospected.