The Study Of Linear Regression Analysis Of Heteroscedasticity Based On Compositional Data

Heteroscedasticity often appears in linear regression model,when the random error term is heteroscedastic,generalized least squares method is an effective method to estimate the regression parameters,and the estimation of random error term variance is the most important issue.In Euclidean space,two-stage estimation based on grouped data is instable because the number of group is uncertain,and this method will lead to the result that a large number of sample information loss.However,the variance estimation based on orthogonal array can enlarge the sample size.Therefore,we can get a more accurate estimate if we combine these two methods.Compositional data often occurs in the economic,geographic,drugs,and some other disciplines.The most general way to solve the problem of compositional data is transforming the compositional data into Euclidean data,then the statistical method in Euclidean space can be used to the transformed data.However,with the improvement of compositional data theory,more and more people consider that how to get a statistical inference for composi-tional data directly.When the compositional linear regression model is heteroscedastic,the ordinary least squares method in simplex space will reduce the accuracy of estimation.In this way,we need to get the generalized least square method in simplex space.The main work and contribution of this paper are as follows:First,we mainly introduce the background and significance of of this research,the research status of compositional data and heteroscedasticity,as well as the research contents of this article.Second,we mainly introduce the definition,property,transformation of compositional data,and some existing methods to solve the problem of heteroscedasticity.Next,we improve the method that two-stage estimation based on grouped data using equal-level orthogonal array.Then we study the scope of mixed-level orthogonal array when there are big difference between the independent variables.Finally,we confirm that the proposed method is more accurate from simulation and real example.Then,the generalized least squares method in simplex space is deduced based on the operation defined in simplex space.Then we prove that the generalized least squares method in simplex space is equivalent to the generalized least squares method in Euclidean space.Finally,some simulation and real example are used to indicate that the proposed method is more valid than ordinary least squares method in simplex when the compositional regression model is heteroscedastic.Finally,we summarize the full text and put forward the future research direction in this chapter.