Influence of estimation neighbourhood selection on result of spatial interpolation

The selection of data points to be included in the estimation is a key problem in the application of spatial interpolation. A common practice to define a single search strategy for an entire area being estimated is not always a good approach. What works in certain areas of a particular data set may not work in others. The solution is to restrict the data point selection to a subset of the data, changing with the estimated point, and thus called a moving neighbourhood. Sophisticated neighbourhood algorithms have been devised to reach a compromise between near and far sample point. They usually include all points within the first ring and then more distance points, following the strategy that attempts to sample all directions as uniformly as possible, while keeping the number of points as low as possible. Deciding which samples are relevant for estimation of a particular point may be more important than the choice of an estimation method. What is the optimum design of a moving neighbourhood? This question turns out to be rather complex. Short of the theory presented in the paper can only give some guidelines. (authors)