Not all smoothing techniques have received equal attention. The kernel, , orthogonal series and spline estimators which have been presented up to this point are widely known and there is a well-developed mathematical theory for them. There are two reasons for this. First, these estimators are simple in structure and therefore easy to compute and easy to analyze mathematically. Second, these estimators have a wide field of applicability and are not designed for estimating special features.
The smoothing techniques to be presented in this section have not
received as much theoretical treatment
but are of interest in their own right, since they exemplify how
the nonparametric smoothing method might be adapted to specific contexts.
The list of smoothers presented here is far from being complete, the
interested reader should consult the review article by
Collomb (1981)
for more references.