The Study Of The Consistency Of Estimator For Semi-parametric Regression Model And Non-parametric Regression Model Based On NOD Sequences

The study of theory on NOD sequence have been fully developed in recent years, especially in some important inequality, such as the Rosentha type inequality, Berstein inequality, the moment inequality of NOD sequence and the part and probability in-equality and so on,those make the NOD sequence have been well developed in the field of statistics. As we known, the consistency of sequence is a hot topic in the field of statistics, and it has been developed rapidly in recent decades. But there is a little results about NOD sequence in this side. So we will focus on research the consistency of estimator for semi-parametric regression model and non-parametric regression model based on NOD sequence, and get good results.This thesis is divided into three parts.The first chapter of this article is the preface, the purpose is to describe the origin and value of the problem, the semi-parametric regression model and non-parametric regression model in the problem, concepts, some inequalities and related lemma.In Chapter2, we study semi-parametric regression model yi=xiβ+g(ti)+σiεi,i=1,2,…, n, we integrated the methods of weighted function and least squares, the least squares estimator and weighted least squares estimator of model’s parameter β and the unknown function g are defined. By using the truncating method, and the moment inequalities for NOD sequences and the properties of convex function, the constraints of weight function, we get the p(p>1) th mean consistency, under some mild conditions, which promote the range of moment.In Chapter3of this paper to consider the non-parametric regression model yi=g(xi)+εi, i=1,2,…, n, the estimated gn of the unknown function g is defined. we studied its complete convergence in0<p<1and p>1and under mild conditions we proved its weak consistency, get good results, since independent sequences and NA sequence are specific case of NOD sequence, so those results of independent and NA sequence are generalized by the ones that we obtain.