On a semiparametric regression model whose errors form a linear process with negatively associated innovations

In this article, we are concerned with the regression model y i =x i β+g(t i )+V i (1≤i≤n), where the known design points (x i , t i ), the unknown slope parameter β, and the nonparametric component g are non-random and where the correlated errors , with and negatively associated e i , are random variables. Under appropriate conditions, we study the asymptotic normality for the least squares estimator of β and the nonparametric estimator of g(·). Moreover, strong convergence rates of these estimators are considered. Our results show that the nonparametric estimator of g(·) can attain the optimal convergence rate.

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