Extension And Analysis Of Heteroskedasticity-Consistent Covariance Matrix Estimators

In the linear regression model,the variances of the random error terms are usually assumed equal,but in most cases that is not succeed,we call it heteroskedasticity.When the linear model exists heteroskedasticity,ordinary least squares(OLS)estimator is also unbiased,consistent,and asymptotically submit the normal distribution.However,the co-variance matrix estimator becomes biased and inconsistent.When use the estimator to construct test,there will be a serious consequence in test result.To solve the problem,we need consistently estimate the covariance matrix estimator to make the test based on the estimator will be more precise.Therefore,it is necessary to study the consistent covariance matrix estimator of parameter estimation.The most frequently used methods are heteroskedastic-consistent covariance matrix estimators(HCCMEs),in-clude HCO,HC1,HC2,HC3,HC4,HC5 and HC4m estimators.These HCCMEs are the covariance matrix consistent estimators of unknown parameters,and their core contents all are the covariance matrix estimators of the random error terms.Each HCCME has own advantages and disadvantages,where HC5 and HC4m improve the performance of the other alternative estimators under the cases of high leverage points and no leverage points,respec-tively.However,it implies the weakness of HC4m and HC5:the t test whose test statistic uses the HC4m estimator is more liberal than the one which is HC5-based when the data contain high leverage points;on the other hand,when there is no high leverage point in the data,HC5 has a poorer behavior than HC4m.So in this paper,we try to combine them and obtain a new estimator HC5m,which delivers inferences through associated test and is reli-able regardless of the existence of high leverage points.All the above-mentioned HCCMEs mainly focus on the statistical inference,various HCCMEs have different effects in t test.However,in the aspect of model prediction and model fitting,all HCCMEs have a minor distinction,even if for HC5m.The article proves the two conclusions through abundant simulation experiments.This paper is divided into five chapters:Chapter I:Introduction.We mainly introduce background,goal and significance of this research,related knowledge of the heteroskedasticity phenomena about the domestic and foreign research,and research contents in this paper.Chapter II:Introduction of heteroskedasticity-consistent covariance matrix estimators.We introduce the general linear regression model and heteroskedastic estimation methods(HCCMEs),and the deficiencies of existing methods are pointed out.Chapter III:The improvement of heteroskedasticity-consistent covariance matrix esti-mators based on HC4m and HC5.According to advantages and disadvantages of HC4m and HC5,we propose a new estimator,and new HCCME has a better finite sample behavior than other estimators regardless of the existence of high leverage points,which is proved by simulation experiments and instance analysis.Chapter IV:Analysis based on heteroskedasticity-consistent covariance matrix estima-tors.Through abundant simulations and case analysis,we find that various HCCMEs are very closed in terms of model prediction and model fitting.Chapter V:Conclusion and expectation.The main research contents of this paper are summarized,and the future research works are pointed out.