Statistical Research And Application Of Semiparametric Model With Missing Covariates

Missing Data denotes that during data collection people only observe part of the values for some reason and obtain the data which has missing values.The phenomenon of data missing is easy to happen and has attracted more and more attention and research.Semiparametric model is a significant statistical model with many theories and wide applications, it has the advantages of both parametric model and nonparametric model and it is widely applied into economics,management,financial engineering,. Partially linear model is an important semiparametric model and it is the main research object fo this paper.Scholars mainly focus on the estimation of model parameter and its asymptotic properties when researching semiparametric model with missing data and have obtained many academic achievements,but there are few paper considering the serial correlation test on semiparameter model.When conducting regression analysis,for a good fitted model its residuals are white noises,which means its residuals are independent and have no serial correlation,otherwise it may lead to many troubles even cause model misused.Based on above considerations,in this paper we mainly research the serial correlation test on partial linear model with missing covariates.Linear model is a fundamental model in statistics and the research on the linear model can help and inspire other model research.So before researching partial linear model,we first research the serial correlation test on linear model with missing covariates and propose the empirical likelihood ratio test,the results of simulation suggest this test method is efficient.On the base of linear model research,we further consider the serial correlation test on partial linear model with missing covariates. First,we deal with the missing covariates using imputation, then estimate the model’s parameter and function. Second, introducing empirical likelihood method.We establish the the empirical likelihood ratio test statistics and demonstrate its asymptotic property under hypothesis and assumptions. Finally,the results of simulation indicate this test method is quite efficient.