  In this paper we investigate the problem of estimating the regression
function in models with correlated observations. The data is obtained from
several experimental units each of them forms a time series. We propose a new
estimator based on the inverse of the autocovariance matrix of the
observations, assumed known and invertible. Using the properties of the
Reproducing Kernel Hilbert spaces, we give the asymptotic expressions of its
bias and its variance. In addition, we give a theoretical comparison, by
calculating the IMSE, between this new estimator and the classical one proposed
by Gasser and Muller. Finally, we conduct a simulation study to investigate the
performance of the proposed estimator and to compare it to the Gasser and
Muller's estimator in a finite sample set.
