Asymptotic Properties Of Wavelet Estimators In Fixed-design Partially Linear Errors-in-Variables Models With Long-Range Dependent Errors

Partially linear EV model is a very important statistical model.The assumption that the random variables are independent is not very suitable in many cases,so people often study the case of dependent random variables,the asymptotically almost associated sequence in this paper is an important one.In this paper,the most important model use the wavelet estimation method to study the wavelet estimation model with the parametric estimator ?and nonparametric estimator g(·)have been given and to get the related large sample properties with the practical applications are given.The specific research contents are as follows:In the second chapter,we study the weak consistency of wavelet estimation of ?,g(·)when the errors{?i} are long dependent and the measurement errors {ui} are independent and long dependent,and the practical problems of the consumer confidence index in China are studied,and the results obtained from the examples are very good,which shows that the conclusions proved in this paper are useful in practice.In chapter 3,under the condition that the errors {?i} are long dependent and the measurement errors {ui}are mutually independent and long dependent,we study and obtain the asymptotic representation of parameter wavelet estimation,the weak convergence rate of parameter,the asymptotic distribution of non-parameter and the weak convergence rate.We generalize the wgeneralize theeak consistency and mean square consistency of parameter ? and function g(·)estimation in partial linear model in literature[11],and we also generalize the asymptotic representation of parameter estimator ?,the asymptotic distribution of parameter and nonparameter g(·)and the weak dependence rate in literature[12].