Statistical Diagnostics For Joint Mean And Variance Models

The statistical diagnosis method appeared in the 70s of last century.It is an important branch of statistical inference.As the name implies,statistical diagnosis is a diagnosis of statistical analysis,that is,the data,model and related statistical methods are analyzed and identified possible problems with the help of diagnostic statistics.Then solve the problem,make statistical inference able to get closer to the real situation better,and reveal the objective law of the research object more accurately.Most of the current statistical diagnosis methods are based on the mean regression model,which usually requires homogeneity of the observed data.However there are often some data with heteroscedasticity in practical applications.If the influence of heteroscedasticity cannot be eliminated,it is not appropriate to use this mean regression model to process heteroscedasticity data so that it is difficult to get reasonable results.Therefore,it is necessary to model variance.In this case,this paper is based on normal distribution,and establishes a regression model for the mean and variance parameters,and studies the statistical diagnosis of the combined mean and variance model in detail.The main researches are as follows:(1)Under the maximum likelihood estimation theory,we study the statistical diagnosis of joint mean and variance models based on data deletion method.Meanwhile,based on the likelihood distance,which is diagnosed by means of mean drift disturbance and variance weighted disturbance respectively.(2)In the framework of Bayesian theory,the Bayes statistical diagnosis of joint mean and variance models is first proposed.The estimated values of mean and variance models are obtained by Gibbs sampling and MH algorithm.K-L distance,L1 distance,?2(chi-square)distance and Cook posterior mean distance are studied based on the data deletion method.(3)A common way of data deletion is to delete a sample point or some sample points and estimate the parameters of the established model,however the Pena distance research on the effort of deleting each points in the sample regression for a given sample points and predicted values.It is also a diagnostic method based on data deletion and an important complement to diagnostic statistics.In this paper,the Pena distance is applied to the joint model,is used to study the effect of the Pena distance of the joint model.At the same time,the results are compared with the results of the first two parts of the paper.The above three parts are simulated and analyzed by Monte Carlo method.All the outliers we set up are diagnosed.At the same time,the above diagnostic methods are analyzed with two case data and compared with the diagnostic results in the related references.It shows that the method proposed in this paper is effective.