Influence Analysis Of Generalized Partially Linear Models With Local Modal Regression

Influence analysis,as an important branch of modern statistical diagnostics,is an important part of data analysis,analyzes the influence of data points on the statistical inference of model parameters and has been used widely in many fields such as Economy and Finance,Biomedical Science,Quality Supervision and so on.And Generalized Partially Linear Models(GPLM)combines the advantages of Parametric Regression and Non-parametric Regression,which has a good fitting for all kinds of data.But,when the data distribution is skewed or heavy-tailed,the common method of Mean Regression has a bad fitting for these data,then,the Modal Regression proposed by Yao and Li has solved this problem and shows many advantages.Yang and Yang extend modal regression and apply to the semi-parametric partially linear single-index models based on what Yao and Li have done,known as local modal regression.But few people has extended local modal regression to PLM(partially linear model)and GPLM,especially on the influence analysis of the models.On the basis of what others have done,the contents of this thesis are as follows:(1)This thesis extends local modal regression to PLM and GPLM on the foundation of what Yang and Yang have done.Firstly,the local linear approximation has been used for the nonparametric part of the models,non-parametric kernel density method has been used for estimating the mode of distribution function,and the modal expectation-maximization algorithm has been used for estimating parameter.Then numerical simulations are carried out via setting the different link functions such as Canonical function,Logarithmic function and Logic function for GPLM with local modal regression and the results of simulations show that the bias of the estimator for parameters are controlled with 6%.(2)Influence analysis has been done for GPLM with local modal regression,with inferring the corresponding diagnostic statistics for case-deletion model,modal-shift outlier model and perturbation model.Setting different link functions such as logarithmic function and logic function have been simulated,this thesis also have a real data analysis for Mouthwash data.