Non-parametric estimation of the average growth curve with a general non-stationary error process

The non-parametric estimation of the average growth curve has been extensively studied in both stationary and some nonstationary particular situations. In this Note, we consider the statistical problem of estimating the average growth curve for a fixed design model with a non-stationary error process. The non-stationarity considered here is of a general form, and this note may be considered as an extension of previous results. The optimal bandwidth is shown to depend on the singularity of the autocovariance function of the error process along the diagonal.