Some Strong Limit Theory For WOD Random Variables And Its Application

The class of wide orthant dependent(WOD,in short)random variables includes independent random variables,negatively associated(NA,in short)random variables,negatively orthant dependent(NOD,in short)random vriables and extended negatively dependent(END,in short)random vriables.It has wide applications in insurance and financial mathematics,reliability theory,survival analysis and other fields.This thesis focuses mainly on some strong convergence properties for WOD random variables,such as complete convergence,complete moment convergence and almost sure convergence,and establish the consistency of the estimator of nonparametric regression model.In Chapter 2,we investigate the complete convergence and complete moment convergence for sums and weighteds sums of WOD random variables.Based on identical distribution,by using the Fuk-Nagaev type probability inequality and the method of truncation,we establish the complete convergence for sums of WOD random variables.As an application,we get the complete moment convergence for sums of WOD random variables.The results generalize the corresponding ones of Chen and Sung[15]and Qiu and Chen[57]for independent random variables.Based on these results,we investigate the complete convergence and complete moment convergence for weighteds sums and random weighteds sums of WOD random variables.In Chapter 3,we study the complete convergence and complete moment con-vergence for maximal partial sums and weighteds sums of WOD random variables.Based on identical distribution,by using the Rosenthal type moment inequality and the method of truncation,we establish the complete convergence for maximal partial sums and weighteds sums of WOD random variables.As an application,we get the Marcinkiewicz-Zygmund type strong law of large numbers.The results generalize and improve the corresponding ones of Wang et al[74]and Ding et al[2].In Chapter4,we investigate the complete convergence and complete moment con-vergence for weighteds sums of arrays WOD random variables.Based on nonidentical distribution,firstly,by using the Marcinkiewicz-Zygmund type moment inequality and the method of truncation,we establish the complete convergence for weighteds sums of arrays WOD random variables.We also obtained the complete convergence for weight-eds sums of WOD random variables as a corollary.The results generalize and improve the corresponding ones of Qiu[7].Next,by using the result of Wang[77]'s,we establish the complete convergence for maximal partial weighteds sums of arrays WOD random variables which generalize the corresponding ones of Chen and Sung[17]for NOD ran-dom variables.And the method is different from the common one.Finally,by using the Rosenthal type moment inequality and the method of truncation,we establish the complete convergence and complete moment convergence for weighteds sums of arrays WOD random variables under the much more general condition.The results generalize the corresponding ones of Ko[40]for arrays PNQD random variablesIn Chapter5,we study the complete moment convergence for WOD linear pro-cesses with random coefficients.By using the Marcinkiewicz-Zygmund type moment inequality and another moment inequality,we establish the complete moment conver-gence for WOD linear processes with random coefficients.The results generalize the corresponding ones of Hosseini and Nezakati[37]for END linear processesIn chapter 6,we mainly discuss the application of WOD random variables in nonparametric regression models.We study the complete consistency of estimator in nonparametric regression models under WOD errors.We also give numerical simulation to verify its theoretical results that are indeed effective.