Abstract
Consider the heteroscedastic semi-parametric model y i = x i β +g(t i ) + σ i e i (1 ≤ i ≤ n), where , the design points (x i , t i , u i ) are known and non random, g(·) and f(·) are unknown functions defined on closed interval [0, 1], and the random errors e i are assumed to be a sequence of stationary α-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 β. Also, the asymptotic normality of the estimators of g(·) and f(·) is considered. Finite sample behavior of the estimators is investigated via simulations as well.
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