The Statistic Inference Of Semi-parametric Partially Linear Varying-coefficient Model

This paper mainly uses the technique of principal component analysis,kriging regressing imputation,Group Lasso and Bootstrap to solve the problems of the estimation of semi-parametric model such as multi-collinearity,missing data and group data.Furthermore,we investigate the estimation of semi-parametric model on the small sample condition and provide the corresponding proprieties.The detailed work is as follows:For the problem of multi-collinearity,this paper studies the back-fitting estimation of semi-parametric partially linear varying-coefficient models on the basis of principal component analysis.In order to overcome the multi-collinearity and have better estimation efficiency,we apply principal component analysis to semi-parametric partially linear varying-coefficient models.That is to say,we use principal components as new variables and then we obtain the estimators of original parametric component and nonparametric component by the method of back-fitting estimation.Furthermore,we provide some statistic inferences about the estimators.For the problem of missing data,we investigates a class of estimation problems of the semi-parametric model with missing data.On the basis of previous methods utilized to deal with the robustness of missing data in the references cited therein,we propose a modified imputation estimation approach called Kriging-regression imputation.Compared with classic imputation methods,the new proposed method not only makes more use of the data information,but also has better robustness.In order to further improve the robustness,LASSO technique is introduced into Kriging-regression imputation and we provide the corresponding improvement results.Model estimation and asymptotic distribution of the estimators are also derived theoretically.Numerical experiment is also provided to show the effectiveness and superiority of our proposed method.For the problem of missing data existed in practical application of semi-parametric model,this paper discusses variable selection and imputation estimation of semi-parametric partially linear varying-coefficient model in that case where there exist missing responses for cluster data.Combined the idea ofcomplete-case data and a discussion of shrinkage estimation is made on different cluster.In order to avoid the biased results as well as improve the estimation efficiency,this article introduces Group Least Absolute Shrinkage and Selection Operator(Group Lasso)to semi-parametric model.The method can conduct nonparametric estimation and variable selection in a computationally efficient manner.For the small sample problem of semi-parametric model,we investigate the bootstrap estimation of semi-parametric model and provide the corresponding estimation results as well as statistics proprieties.