Complete And Complete Moment Convergence For Weighted Sums Of Random Variables And Its Application In Nonparametric Regression Models

Probability theory is an important part of mathematics,and the theory of probability limit plays an important role in probability theory,many statisticians have studied it systematically,probabilistic limit theory has been mature.With further study,scholars found that END variables and WOD variables have important research value in the dependent sequence,Many scholars have studied it.In this paper,by some properties and inequalities of existing dependent sequences,the related convergence of END random variables and WOD random variables and their applications are further studied.The main contents of this paper are as follows.Chapter 1,This chapter introduces the research background,relevant concepts and definitions,as well as the important inequalities needed in the process of proof.Chapter 2,by using Rosenthal maximum moment inequality of WOD random variables and the truncation method of random variables,the complete convergence for weighted sum of WOD random variables is obtained,and the M-Z type strong law of large numbers of WOD random variables is obtained.Chapter 3,by using Rosenthal type moment inequality for weighted sums of END random variable and truncation method of random variable,the complete moment convergence for order weighted sums of END random variable is obtained.Chapter 4,The application of WOD random variable in non-parametric regression model is obtained by using the results obtained,and numerical simulation is carried out.The simulation results verify the validity of the theoretical results.Chapter 5,it summarizes the innovation and shortcomings of the article.