Parameter Estimation And Bayesian Analysis Of Missing Skew-Normal Mixture Of Experts Models

In analyzing real data in various fields such as finance,healthcare,social sciences,and environmental sciences,the assumption based on homogenous population and normal errors cannot identify the skewed features and heterogeneity of the data.On the one hand,ignoring the heterogeneity of the data often leads to underfitting,resulting in inadequate predictive power of the model.Mixture of Experts(Mo E),a popular framework in statistical and machine learning fields,is often used to model the heterogeneity of the data for regression,classification,and clustering,and can better capture the different features of the dataset.On the other hand,ignoring the skewed features of the data leads to information loss.Assuming that the data follows a symmetric distribution such as the normal distribution cannot capture the skewness of the data well in real-world applications.It should be noted that due to the skewed characteristics of the data,the mode,as the ”most frequent level” marker,can better characterize the trend of the dataset compared to the mean and median,and is not affected by outlier observations,ensuring its robustness.Finally,missing data is inevitable in many fields such as data management.In statistical modeling,ignoring this problem will result in the loss of a large amount of useful information,and even lead to unreliable results.As the same time,in practical applications,some statistical problems can be transformed into special cases of missing data,such as considering latent variables as essentially missing data in Bayesian analysis.Therefore,this thesis proposes a missing skewed normal mode mixture of experts model,and studies the estimation of the model from both likelihood and Bayesian perspectives.Specifically,the research work carried out in this thesis is as follows:Firstly,this thesis investigates the parameter estimation of the skewed normal mode mixture of experts model under random missing response variables.A hierarchical mode regression imputation method is proposed,and its performance is compared with three popular machine learning imputation methods(support vector machine imputation,random forest imputation,and BP neural network imputation)and three statistical imputation methods(hierarchical mean imputation,mode regression imputation,and hierarchical mode regression imputation)through simulation experiments.Finally,the feasibility of the hierarchical mode regression imputation method is demonstrated through real data of Shanghai air quality index(AQI),where the parameter estimation of the skewed normal mode mixture of experts model is studied under complete and missing data.Secondly,this thesis proposes a skew-normal mode mixture expert model under the Bayesian framework.By representing the mixture skewed normal hierarchically and utilizing independence to simplify computations and improve efficiency,a hierarchical Bayesian model is constructed.A mixed sampling algorithm using Gibbs sampling and M-H algorithm is employed,and simulation experiments are conducted to demonstrate the robustness of the proposed model under different prior information.As the proposed model includes the special case of the normal mixture of experts,the results show that when the skewness is high,the proposed model has better numerical performance in dealing with skewed data compared to the normal mixture of experts.Finally,the practicality and feasibility of the proposed method are demonstrated through real data from the real estate industry.