Difference Estimation Of Semi-parametric Models And Its Applications

In the paper,we consider the following semi-parametric regression model y=X?+g(t)+?,where y is a n×1 observed vector,Xis a n×p known matrix,r(X)=p,? is a p×1 unknown parameter vector,g(t)is a smooth continuous unknown function,? is a n×1 error vector with E(?)=0 and Cov(?)=?2I.The semi-parametric regression model is widely used,many scholars have used a variety of methods to conduct in-depth research on the semiparametric regression model and related issues.This paper uses the difference method to study the semiparametric regression model,and mainly study the following three contents:In Chapter 2,in order to eliminate the non-parametric effects in the semi-parametric model,and improv the accuracy of parameter estimation,a difference operator is introduced in this model.Thus we obtain the following model:Dy=DX?+D?.According to the balanced loss function,optimal linear unbiased estimators of the parameters are obtained.The relative efficiency of the estimators are redefined by the risk function,and the parameter difference estimators are better than the least square estimators.Then by the weight function method,the non-parametric estimation is given under the model.At the same time,the estimation compared with the nonparametric estimation under least squares,and the theoretical results of the champter are illustrated.Finally,a simulation example is given to illustrate the validity of the results.In Chapter 3,we mainly study diagnose and testing of outliers under the semi-parametric model.Firstly,the model is transformed into a linear model,so that the error in the above model satisfies the Gauss-Markov hypothesis.Secondly,by the Cook diagnostic statistics,we analyse the points that have a greater impact on the regression model.At then we perform the outlier point test.Finally,a simulation example is given to illustrate the conclusion of this chapter.