Nonparametric estimation of a regression function by delta sequences

A somewhat more general class of nonparametric estimators for estimating an unknown regression functiong from noisy data is proposed. The regressor is assumed to be defined on the closed interval 0, 1]. This class of estimators is shown to be pointwisely consistent in the mean square sense and with probability one. Further, it turns out that these estimators can be applied to a wide class of noises.