Convergence Property Of Widely Orthant Dependent Random Variables And Its Applications

Since the probability limit theory was put forward in the 1950 s,as an important branch of probability theory and mathematical statistics,after the painstaking research of many scholars,the probability limit theory of independent random variables has achieved fruitful research results,and the relevant theories have been very mature.However,the sample data obtained in real life are often not independent,so it is necessary to expand the research results,At present,more and more experts and scholars devote their energy to the study of the properties of dependent random variables.This paper mainly discusses wide dependent(WOD)variables,which include independent variables and some dependent variables.It is a very broad class of variables.In this paper,we first establish the complete convergence theorem and the complete moment convergence theorem for Sung type weighted sum of WOD random variable sequence by using the five-section truncation method and combining Rosenthal type and Marcinkiewicz-Zygmund type moment inequality.On this basis,the marcinkiewicz-Zygmund weighted strong number law is established,and the large number law is simulated numerically.Secondly,the generalized negative quadrant dependent variable(END)is generalized,and the complete convergence theorem and the complete moment convergence theorem of the moving average process generated by the sequence of WOD random variables are obtained,which enriches and improves the probability limit theory of WOD random variables.Finally,the nonparametric regression model with WOD random variable sequence is introduced,and the complete consistency of the estimator under WOD random variable error is discussed in this model,and the complete consistency of the nearest neighbor estimator is obtained.