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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 ${y}_{i}={x}_{i}\beta +g\left({t}_{i}\right)+{V}_{i}$ $\left(1\le i\le n\right)$, where the known design points $\left({x}_{i},{t}_{i}\right)$, the unknown slope parameter $\beta$, and the nonparametric component $g$ are non-random and where the correlated errors ${V}_{i}={\sum }_{j=-\infty }^{\infty }{c}_{j}{e}_{i-j}$, with negatively associated ${e}_{i}$, are random variables. Under appropriate conditions, we study the asymptotic normality for the least squares estimator of $\beta$ and the nonparametric estimator of $g\left(·\right)$. Moreover, strong convergence rates of these estimators are considered. Our results show that the nonparametric estimator of $g\left(·\right)$ can attain the optimal convergence rate.
MSC:
 62G08 Nonparametric regression 62G20 Nonparametric asymptotic efficiency 62F12 Asymptotic properties of parametric estimators