The Research On Test And Estimation Methods Of Heteroscedastic Model

An important assumption in the classical linear regression model is that the model satisfies the homoscedasticity.However,in many practical problems,models do not satisfy this assumption due to the omission of explanatory variables,measurement errors,and the influence of random factors,and so forth.At this time,the model exists heteroscedasticity.When the heteroscedasticity occurs in the model,if the model estimation is continued by using the ordinary least squares method,the accuracy of the model estimation and statistical test results will be reduced,and the predictable result of the model will also have a certain deviation.For an actual problem on linear regression model,whether or not the model has heteroscedasticity can directly affect the model estimation,evaluation and predictable result.The G-Q test is a classical heteroscedastic test method only applicable to the univariate model;the model can use the G-Q test on the premise that there is an increasing or decreasing correlation between the variance of the error term and the independent variable,however,this condition usually be ignored.Conversely,using the G-Q test may result in the opposite test result.Therefore,this paper proposes a K-S heteroscedastic test based on G-Q,which can effectively test the model for heteroscedasticity.When the model does exist heteroscedasticity,the weighted least squares method is a commonly used estimation method when the covariance matrix of the model error term is known.However,when the covariance matrix of the error term of the model is unknown,the two-stage method of the heteroscedastic model will lose the sample information,and there is some irrationality in the method for determining the most dominant independent variable causing the heteroscedasticity of the model.Therefore,this paper proposes a twostage estimation of heteroscedastic model based on HCCME,which can obtain model estimation very effectively.In this paper,the effectiveness of the above two new methods is proved by a large number of numerical simulations and case studies.This paper is divided into four chapters:Chapter1: Introduction.The research status and significance of heteroscedastic test and heteroscedastic model estimation in linear regression model are introduced,and the main contents of this paper are given.Chapter 2: K-S heteroscedastic test based on G-Q.The main contents of this chapter include the preparation knowledge of K-S test and G-Q test and the newly proposed K-S heteroscedastic test based on G-Q.Chapter 3: Two-stage estimation of heteroscedastic model based on HCCME.The main contents of this chapter include the preparation knowledge of HCCME and grouping twostage estimation of heteroscedastic model and the two-stage estimation of heteroscedastic model based HCCME.Chapter4: Conclusion and Future Work.The main contents of this paper are summarized and the future research directions are given.