Statistical Inference For Mode,Mean And Median Regression Models Based On Skew-normal Data

Skewed or asymmetric data often appear in the research fields of finance,economy,biomedicine,engineering technology and social science.However,most of the methods of analyzing skewed data are focused on the mean regression model,which often ignores the skewed characteristics of the data and leads to some unreasonable and even wrong conclusions.Therefore,according to the characteristics of mean,mode and median in skew-normal(SN)data,this dissertation simultaneously establishes the mean,mode and median regression models,and investigates the model parameter estimation,and further explores the parameter estimation and statistical diagnosis problems in the case of multicollinearity of data.This dissertation mainly studies the following three aspects:Firstly,in order to capture the "average","medium" and "maximum" levels in the skew-normal data,the mean,median and mode regression models are constructed,and the expectation maximization(EM)algorithm based on Newton Raphson iteration is used to estimate the unknown parameters of the model.Secondly,for skew-normal data,when the data has multicollinearity,we use EM algorithm and ridge estimation method to investigate the parameter estimation method of mean and mode regression model and the selection method of shrinkage parameters.Thirdly,Pena distance statistics are used to conduct statistical diagnosis research on mean,median and mode regression models under skewed normal data,and Pena distance expressions of each model and diagnosis methods of high leverage outliers are obtained.The likelihood distance,Cook distance and Pena distance statistics are obtained by using EM algorithm,gradient descent method and data deletion model.The results of Monte Carlo simulation and real data analysis show that the effect of parameter estimation of mode regression model is better than that of mean and median regression model under skew-normal data;Ridge estimation plays a good role in adjusting the estimation of regression model with multicollinearity and skew-normal data;The diagnostic effect of Pena distance is better than that of likelihood distance and Cook distance.