The consistency of the estimators in semiparametric regression model based on m -asymptotic negatively associated errors

In this article, we analyze the strong consistency and r-th (r > 1) mean consistency for the estimators βu, n and gu, n of β and g, respectively, based on m-asymptotic negatively associated errors. Furthermore, the convergence rate for the strong consistency of the estimators is also considered. The results obtained in this article extend the corresponding ones for ρ∗-mixing random variables and other dependent sequences.