Asymptotic normality in partial linear models based on dependent errors

In this paper we are concerned with the regression model yi=xiβ+g(ti)+Vi(1⩽i⩽n) under correlated errors Vi=σiei and Vi=∑j=-∞∞cjei-j, where the design points (xi,ti) are known and nonrandom, the slope parameter β and the nonparametric component g are unknown, {ei,Fi} are martingale differences. For the first case, it is assumed that σi2=f(ui),ui are known and nonrandom, f is unknown function, we study the issue of asymptotic normality for two different slope estimators: the least squares estimator and the weighted least squares estimator. For the second case, we consider the asymptotic normality of the least squares estimator of β. Also, the asymptotic normality of the nonparametric estimators of g(·) under the two cases are considered.