Moment Inequalities Of M-NA Random Variables And Their Applications

After some scholars' painstaking researchs,the probability limit theory has been very rich.From the beginning of the central limit theorem,to inde-pendent random variables,and then to dependent sequence,mixed sequence,all the experts and scholars involved in the heart.Today,many scholars contin-ue to explore the mystery of probability limit theory.As a dependent sequence,the m-NA random variable sequence appear in the researchs.There are some relevant theories about m-NA random variables,this paper is based on the ex-isting research,more indepth study of the relevant properties of m-NA random variables,and give two applications.This paper is divided into seven chapters.Chapter 1,as the beginning of this paper,we introduce some related knowledge of probability limit theory,the background of the research,and the research route.Chapter 2,this chapter introduces the theoretical basis of the whole pa-per,the moment inequalities of m-NA random variables,paves the way for the following research.This chapter mainly introduces how to use NA ran-dom variable moment inequalities to obtain the moment inequalities of m-NA random variables.Chapter 3,we give the properties of weighted sums of m-NA random variables sequences.According to m-NA's three series theorem,we prove the almost sure convergence of weighted sums of m-NA random variable sequences.Chapter 4,based on the moment inequalities of m-NA random variables,with the help of truncated method of random variables,research the complete moment convergence of m-NA random variables.Chapter 5 and chapter 6 are the practical applications of the properties of m-NA random variables.Based on the results of the second chapter,we study the large deviation of the least squares estimator of the nonlinear regression model under the m-NA random variable errors and the strong consistency of least squares estimator of the multiple linear regression model under the m-NA random variable errors.Chapter 7,as the conclusion of the whole article,summarizes the process of writing this paper,as well as the merits and shortcomings of this paper.