Journal of the
Korean Mathematical Society JKMS

Consider the nonparametric regression model $Y_{ni} = g(x_{ni}) + \epsilon_{ni}$ ($1 \le i \le n)$, where $g(\cdot)$ is an unknown regression function, $x_{ni}$ are known fixed design points, and the correlated errors $\{\epsilon_{ni}, 1 \le i \le n \}$ have the same distribution as $\{V_i, 1 \le i \le n\}$, here $V_t=\sum^\infty_{j=-\infty}\psi_j e_{t-j}$ with $\sum^\infty_{j=-\infty}|\psi_j|<\infty$ and $\{e_t\}$ are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of $g(\cdot)$. As corollary, by choice of the weights, the Berry-Esseen type bound can attain $O(n^{-1/4}(\log n)^{3/4})$.

Keywords: nonparametric regression model, negatively associated random variable, Berry-Esseen type bound

MSC numbers: 62G08