The Consistency Of Estimators In Nonparametric And Semiparametric Regression Models Under Negatively Associated Data And Its Application

Regression analysis is a statistical analysis method used to study the relationships between random variables.It can help us explain some phenomena,and can predict future trends.Regression models can be used to describe some phenomena in economics,biomedical,industrial,agricultural and other fields.However,in real life,many practical problems are more complex,if linear regression is adopted,the fitting effect is generally not ideal.In this case,we can consider nonparameter regression model and semi-parameter regression model.Consequently,it is crucial to study the asymptotic properties of model estimators.This paper study the consistency of estimators in nonparameter and semi-parameter regression models and applies them to practical problems.This paper mainly studies the consistency of estimators in nonparameter and the semi-parameter regression models under NA(Negatively Associated)random errors.Specifically,the research contents include three parts as follows.(1)In order to obtain the consistency of the model estimators,we first discuss the convergence properties for weighted sums of negatively associated random variables.The convergence theorem for the weighted sum of NA random variables is obtained by using some probability inequalities and the condition of stochastic domination.The results improve and extend the corresponding ones of Zhang,Chen and Sung.(2)Based on the established theoretical results,we further study the consistency for the weighted estimator of nonparameter regression model under NA random errors,and we also study the consistency for the G-M estimator(an estimator involved with integral form)of nonparameter regression model under NA random errors,then present some numerical simulations of the two estimators in R software.(3)Finally.we consider the semi-Darameter reg'ression model u(n)=xi(n)?+g(ti(n))+?i(n),i=1,2,..,n,n?1,based on the theoretical results above again,when the errors are NA random variables,we study the consistency for the least squares estimator of unknown parameter ? and the weighted estimator of unknown function g in the semi-parameter regression model,then give its application and present some numerical simulations in R software,we also give an example analysis of applying the semi-parameter regression model to solve practical problems.