Empirical Likelihood Inference For Response Difference In Partical Linear Model With Missing Data

Missing data often occurs in real life.For example,in the fields of medical research and industrial production,missing data often occurs.When the data is missing,the usual statistical methods cannot be directly applied for data analysis,it is necessary to complete the missing values,thus get the complete sample,and then do inference by using the usual statistical methods.The empirical likelihood is a nonparametric statistical inference method,which has a sampling property similar to bootstrap.This method has many outstanding advantages compared with the classical statistical method.For example,the confidence interval constructed by the empirical likelihood method has the advantages of domain retention,transformation invariance,and the shape of the confidence interval determined by the data itself.There are also advantages of Bartlett rectification and no need to construct axis statistics.In this thesis,we study the empirical likelihood problem for response mean difference in partial linear model with missing data.Firstly,the partial linear models have missing response variables,and the inverse probability weighted imputation is used to imput the missing values,and obtain two complete sample data.Secondly,the empirical log-likelihood ratio statistic of the response mean difference is constructed.Finally,the limit distribution of the empirical loglikelihood ratio statistic is obtained,and the confidence interval of two response mean difference is constructed.