Some Limiting Properties Of Negatively Superadditive Dependent Random Arrays And Its Application In Nonparametric Model

The class of Negatively Superadditive Dependence(NSD)random variables includes independent random variables,Negatively Associated(NA)random variables as special cases.It has wide applications in financial mathematics,complexity systems,reliability theory and other fields.This dissertation is devoted to the study of some limiting properties of NSD random arrays and its application in nonparametric regression models,the conclusions obtained extend and improve the existing relevant results.The main contents of this dissertation are as follows:Firstly,by utilizing the Marcinkiewicz-Zygmund(M-Z)inequality,Rosenthal type inequality of NSD random arrays and truncated method,the weak convergence,the~rL convergence and the complete convergence for maximum weighted sums of NSD random arrays is discussed.Secondly,by using the Kolmogorov exponential type inequality of NSD random arrays and truncated method,the complete f-moment convergence for maximum weighted sums of NSD random arrays is studied.Thirdly,by exploiting the M-Z inequality,Rosenthal type inequality of NSD random arrays and truncated method,the weak convergence,the complete f-moment convergence for Sung’s type maximum weighted sums of NSD random arrays is obtained.Finally,the application of NSD random arrays in nonparametric regression model is studied by using the results obtained,and numerical simulation is carried out.The simulation results verify the validity of the conclusions.