Consistency Of Nonparametric Estimators Base On NSD Random Sequences

NSD random sequences contain NA random sequences and have many important applications in practical problems,such as in social sciences,finance,insurance,actuarial,etc.In this paper,we mainly study the consistency of density kernel estimator,nonparametric regression function estimator and nearest neighbor density estimator for unknown density function of NSD sample sequences,such as the weak consistency,the strong consistency and the strong uniform consistency,which extend and improve some results in existing literatures.The specific research contents as follows:In Chapter 1,the study background and methodology of the unknown density estimator are concerned,the research status of domestic and abroad about NSD random sequences are stated,and the classification of consistency are also introduced.The main several inequalities and lemmas of thesis are explored.In Chapter 2,by using the Bernstein inequality,Rosenthal inequality and the nature of NSD,we obtian the pointwise strong consistency,the strong uniform consistency and the moment consistency about the kernel estimator of the density function.In Chapter 3,with the random error of arrays of rowwise NSD,the estimation of the nonparametric regression function is considered.Under certain conditions,the strong consistency of the estimator of the nonparametric regression function is obtained.The numerical simulation diagram of the weighted estimator is made by R software.In Chapter 4,by using the inequality and the properties of NSD,we obtian the weak consistency,strong consistency and uniformly strong consistency for the nearest neighbor estimator of density function.