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On a semiparametric regression model whose errors form a linear process with negatively associated innovations. (English) Zbl 1098.62044
Summary: We are concerned with the regression model y i =x i β+g(t i )+V i (1in), 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 V i = j=- c j e i-j , with 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.
62G08Nonparametric regression
62G20Nonparametric asymptotic efficiency
62F12Asymptotic properties of parametric estimators