Research On Heteroscedasticity Estimation Based On Nonparametric Method

In classical linear regression,it is usually assumed that the variance of each random error term is equal.However,in the research of the practical problems such as cross-section data,this assumption cannot be guaranteed very well,that is,the random error term has heteroscedasticity.The existence of heteroscedasticity will cause damage to the test and prediction result of the model.Therefore,the key to solving this problem is to find the appropriate method which could process the heteroscedastic problem.The commonly used method for solving the heteroscedasticity problem is the generalized least squares method.When the covariance matrix of the error term is known,it is called the weighted least squares method(referred to be WLS).The WLS method is only practical when the heteroscedasticity form is known.But the variance of the error term is unknown in general,so the estimated weighted least squares method is widely used.Since the nonparametric method gives a more efficient estimation of variance when the form of heteroscedasticity is unknown,this thesis considers a nonparametric estimation in the estimation of the covariance matrix.In the heteroscedasticity model,if the regression coefficient is still estimated by the ordinary least squares(OLS)method,although the estimator can still guarantee unbiasedness and consistency,the covariance matrix estimation is no longer an unbiased estimation.It will affect the test of the model.To solve this problem,domestic and foreign scholars have proposed heteroscedasticity-consistent covariance matrix estimation(HCCMEs)methods,including HC0,HC1,HC2,HC3,HC4 and so on.As the consistent estimator of the parametric covariance matrix,these methods have been widely used in various modern researches.Based on the construction method of HCCMEs,the weighted heteroscedasticityconsistent covariance matrix estimation(WHCCMEs)derived from the residuals of the estimated weighted least squares(EWLS).The effect is better in the model test,but the choice of weight function is a little limited,and only four forms of WHC0,WHC1,WHC2 and WHC3 are given,which are not comprehensive enough and can be further improved and expanded.Considering that the HCCMEs method is derived from the residual term of the OLS estimator,and the OLS estimator is affected by the outliers in the observations,the robustness is not high.Therefore,the HCCMEs estimators are also less robust in the test of regression coefficients under the heteroscedasticity when there are outliers in the sample.Based on this deficiency,this paper improves it combined with the validity of the nonparametric estimation method.The work done in this thesis is as follows:Firstly,a new heteroscedastic estimation method,KNW method,is proposed based on N-W estimation.And the simulation experiment and case analysis are carried out to prove the accuracy of the method.Secondly,four nonparametric estimators are given for the covariance matrix of the error term,and then the weighted least squares estimation(EWLS)of the regression coefficients is obtained by using different weight function matrixs.The test results of the model under different methods are compared.And new weighted heteroscedasticity-consistent covariance matrix estimations are proposed.Thirdly,considering the robustness of the estimation of the covariance matrix,the robust estimation of the regression coefficients,Least Median of Squares(LMS)and Least Trimmed Squares(LTS)are introduced.And two robust heteroscedasticity-consistent covariance matrix estimations are proposed in combination with nonparametric methods.The robustness of the two methods is verified by the stochastic simulation and case analysis.Finally,the paper summarizes the full text and gives the future research direction.