The Research Of Asymptotic Properties Of Parametric And Nonparametric Estimators For Regression Models With END Errors

Research on the properties and applications of dependent random vari-ables has always been a hot issue attracting by many scholars.The concept of END random variables originates from financial risk research.It contains many dependent structures,such as NA,NOD,NSD and other random vari-ables.Based on the probabilistic properties of END random variables,the parameter least-squares(LS)estimation problem of nonlinear regression mod-el,the unknown function weighted estimation of non-parametric regression model and the parameter LS estimation of multivariate linear model are dis-cussed and some consistency results are obtained under the END errors.The structure of this thesis is as follows.In the first chapter,on the one hand,we present nonlinear regression models,nonparametric regression models,and multiple linear regression mod-els and their brief introductions.On the other hand,we give an introduction,examples and background knowledge of the dependent sequence END.Then,the main research work of this chapter is given:based on the END error,the consistency of the LS estimation of non-linear regression model,the weight-ed estimation of non-parametric regression model and the LS estimation of multivariate linear model are studied,respectively.In the second chapter,we study the large deviation property of the LS estimator of the nonlinear regression model based on the END errors with the help of truncation method and exponential inequality of the END sequence.Under the general conditions,we establish some large deviation results for the LS estimator of the nonlinear regression parameter,which can be applied to obtain a weak uniform consistency and a complete convergence rate for this estimator.In addition,some examples and simulations are provided in this chapter.In the third chapter,we study the complete consistency of the estimator in the nonparametric regression model based on the END errors and obtain the complete convergence rate of the estimator.In addition,the rth-mean consistency and complete consistency of the LS estimator of the multiple linear regression model are obtained.Some examples and simulations are presented for illustration in the last part.In the fourth chapter,we give a summary of this thesis.