Kernel interpolation

In mathematics, the task of interpolating observed data has a long history. Recently, this task has gained even more attention, also from a statistical point of view, as there are many data situations, where either there is no random error (e.g. computer experiments) or the underlying data generating process is very precise such that a repetition will yield the same numerical result. Here we present a new approach to data interpolation which is related to kernel regression estimators and which performs well for small sample sizes in lower dimensions, compared to a standard Kriging approach.