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The problem of estimating the regression function in a fixed design modelswith correlated observations is considered. Such observations are obtained fromseveral experimental units, each of them forms a time series. Based on thetrapezoidal rule, we propose a simple kernel estimator and we derive theasymptotic expression of its integrated mean squared error IMSE and itsasymptotic normality. The problems of the optimal bandwidth and the optimaldesign with respect to the asymptotic IMSE are also investigated. Finally, asimulation study is conducted to study the performance of the new estimator andto compare it with the classical estimator of Gasser and M\"uller in a finitesample set. In addition, we study the robustness of the optimal design withrespect to the misspecification of the autocovariance function.

Trapezoidal rule and sampling designs for the nonparametric estimation of the regression function in models with correlated errors