Parameters Estimation For Robust Mixture Joint Location And Scale Models

We know that there are two important factors influencing the statistics result in the statistics:one is the observing data,the second is the assuming for overall features(distribution,independence,etc).When the abnormal points that can not represent the overall well exist in observation data or research overall does not meet the assumptions some traditional statistical method to some general characteristics,that can be a problem even lead to wrong conclusions.Here some of the more robust statistical methods,a more stable distribution type can reflect more advantage in dealing with such issues,"heavy-tailed distribution" contained abnormal points such as t distribution,Laplace distribution,Pearson type ? distribution are not particularly sensitive to thick tail outliers and deviation from the mean.is a very good stable distribution types,but also reflects the characteristics of the robust statistical method:even if there are a few exceptions,the influence between the deviation caused by the results of distribution and the ideal effect is not much;There are more abnormal points also not lead to wrong conclusions.With the development of the society,the data in each domain our life is becoming more and more complex and diverse,at this time must analysis cluster,heterogeneous mixture model arises at the historic moment,fitting several categories of data with different parameters and proportion distribution.In traditional regression models,we assume the variance of random disturbance are same,but very few data actually meet such requirements.A large number of heteroscedastic data is a breach of the homogeneity of variance assumption.We most use the joint mean and variance model to deal with heteroscedastic data,to understand the source of the variance to control the variance effectively.Now we can also promote the methods,extent the homogeneous joint mean value and variance models to heterogeneous models,making the more extensive application scope.Further,when considering the classification of mixture data is unknown,we can also introduce mixture of expert modeling the mixture proportion,using Logistic regression estimate unknown parameters that affect the mix proportion.In this paper,we take maximum likelihood estimation using EM algorithm for unknown parameters of heterogeneous mixture joint location and scale model based on the t distribution,Laplace distribution and Pearson type VII distribution three robust distribution.The main contents are as follows:Firstly,based on t distribution,establish a mixture joint location and scale parameters model,using EM algorithm and maximum likelihood estimation,the Gauss-Newton iteration algorithm to estimate unknown parameters in the model,and demonstrate the effectiveness of the proposed estimation method through the Monte Carlo simulation.Then try to associate the proposed estimation method with actual life,solve some practical problems.Secondly,based on Laplace distribution,establish a mixture joint location and scale parameters model,using EM algorithm and maximum likelihood estimation,the Gauss-Newton iteration algorithm to estimate unknown parameters in the model,and demonstrate the effectiveness of the proposed estimation method through the Monte Carlo simulation.Then try to associate the proposed estimation method with actual life,solve some practical problems.Thirdly,based on Pearson type ? distribution,establish a mixture joint location and scale parameters model,using EM algorithm and maximum likelihood estimation,the Gauss-Newton iteration algorithm to estimate unknown parameters in the model,and demonstrate the effectiveness of the proposed estimation method through the Monte Carlo simulation.Then try to associate the proposed estimation method with actual life,solve some practical problems.Fourthly,based on the Laplace distribution,in a mixture of expert,establish a mixture joint location and scale parameters model,used the MM algorithm,the EM algorithm,maximum likelihood estimation,the Gauss-Newton iteration algorithm to estimate unknown parameters in the model,and through the Monte Carlo simulation method to demonstrate the effectiveness of the proposed estimation method.Then try to put the proposed estimation method with actual life,solve some practical problems.