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

The probability limit is mainly to study the convergence,the convergence speed and the application in practice of various variables.Although the proba-bility limit theory basic system has been relatively perfect,but it is still rarely implemented in practical applications.In the context of financial insurance,logistics,medicine,etc,it is not just independent sample data,the results established under independent variables can no longer satisfy the needs of re-ality,therefore,experts and scholars have devoted more energy to the study of the properties of dependent variables.This paper focuses on the wide neg-ative orthant dependent(WNOD)variables,which is a very broad variables containing some dependent and independent variables.The first and second chapters are the preparations for this paper.First,introduced the background of the probability limit study and some related definitions,then,in order to prove the need,we propose some inequalities and lemmas.Based on the two most important moment inequalities in the probability limit of the Marcinkiewicz-Zygmund type and Rosenthal type,we propose the maximum inequalities for the weighted sum of WNOD variables.In this paper,some lemmas are proposed by the author himself,and the cor-responding proof process is also given.In chapter 3,first,generalize the theorem of Shen A.T.[1]is,and estab-lish the complete convergence for weighted sums of WNOD variables.The second,generalize and improve results of Wang X.J.et al.[2],Shen A.T.[3]and Chen P.Y.[4],we generalize identical distribution NA random variables and identical distribution END random variables to non-identical distribu-tion WNOD random variables,and the constraint of the weight coefficient{ani,1≤i≤n,n≥1} is weakened,and the results are strengthened,by us-ing method of truncation,we establish the complete convergence for maximal sequence of weighted sums of WNOD random variables.In chapter 4,mainly discusses the application of WNOD random vari-ables in nonparametric regression models,study the complete consistency of estimator in nonparametric regression models under WNOD errors,obtain the complete consistency of the nearest neighbor estimates.Numerical simulation based on the theorem and its corollary in Chapter 3,and the results of the simulation also demonstrate our conclusions.In chapter 5,as conclusion of this paper,summarized the innovation and shortcomings of the article.