The Heteroscedastic Estimation Based On Orthogonal Array

Heteroscedasticity phenomena often presents in the society,economy,biology and other fields.When the homoscedasticity of the linear model is not satisfied,that is to say;the random error variance is not same,we call it heteroscedasticity.When the linear model exists heteroscedasticity,it is heteroscedastic model.Model for testing and predicting will have a huge impact under heteroscedasticity,so how to deal with heteroscedasticity is a very important issue,and the covariance matrix estimation of the random error term is a top priority.Experiment design method is commonly used in industry,agriculture and engineering design.It can increase the production,optimize product quality and reduce production cost.The orthogonal array is the core of experiment design method.The orthogonal array has several excellent statistical properties,such as impartiality,homogeneous dispersion.Using orthogonal array to estimate heteroscedastic model is a new method in recent years,it is a good estimator.But this method also have disadvantages.The disadvantages of existing estimation of orthogonal array in heteroscedastic model include that the dependent variable selection does not dependent on the data matrix,and tolerance selection is too single which is not according to the characteristics of the data itself.So in this paper,we aim at improvingthe heteroscedastic estimation of orthogonal array.This paper is divided into four chapters:Chapter I:Introduction.We mainly introduce goal and significance of this research,related knowledge of the heteroscedasticity phenomena about the domestic and foreign re-search,and research contents in this paper.Chapter II:Covariance matrix estimation under heteroscedasticity.We mainly intro-duce the original covariance matrix estimation in heteroscedasticity-consistent covariance matrix estimation,and heteroscedasticity covariance matrix estimation based on orthogonal array.Finally,the deficiencies of estimation based on orthogonal array is pointed out.Chapter III:The improvement of heteroscedasticity covariance matrix estimation based on orthogonal array.We mainly introduce basic knowledge of orthogonal array,preparation knowledge of estimation,improved covariance matrix estimation method based on orthog-onal array under heteroscedasticity.A lot of simulation experiments and cases analysis are proposed.Chapter IV:Summary and Outlook.The main research contents of this paper are summarized,and the future research direction are pointed out.