Asymptotic Normality of Estimators in Heteroscedastic Semi-Parametric Model with Strong Mixing Errors

Consider the heteroscedastic semi-parametric model y(i) = x(i)beta + g(t(i)) + sigma(i)e(i) (1 <= i <= n), where sigma(2)(i) = f(u(i)), the design points (x(i), t(i), u(i)) are known and non random, g(center dot) and f(center dot) are unknown functions defined on closed interval [0, 1], and the random errors e(i) are assumed to be a sequence of stationary alpha-mixing random variables with mean zero. Under appropriate conditions, we study the asymptotic normality of least-squares estimator and two weighted least-squares estimators of beta. Also, the asymptotic normality of the estimators of g(center dot) and f(center dot) is considered. Finite sample behavior of the estimators is investigated via simulations as well.