The asymptotic properties for the estimators in semiparametric regression model based on $m$-asymptotic negatively associated errors

Abstract

In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on $m$-asymptotic negatively associated ($m$-ANA, for short) random variables. The $r$-th $(r > 1)$ mean consistency, complete consistency and uniform consistency are obtained under some suitable conditions. In order to assess the finite sample performance, we also present a numerical simulation in the last section of the paper. The results obtained in the paper extend the corresponding ones for independent random errors, $\varphi$-mixing and other dependent random errors.