Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models

Abstract

In this paper, a general result on complete moment convergence for arrays of rowwise negatively orthant dependent random variables is obtained. In addition, we present some sufficient conditions to prove the complete moment and complete convergences for the variables. As applications, the complete consistency for the estimators of nonparametric and semiparametric regression models based on negatively orthant dependent errors is established by using the complete convergence that we established. A simulation to study the numerical performance of the consistency for the nearest neighbor weight function estimator in semiparametric regression model is given. Our results generalize and improve some corresponding ones for independent random variables and negatively associated random variables.