A distance-based model for spatial prediction using radial basis functions

In the context of local interpolators, radial basis functions (RBFs) are known to reduce the computational time by using a subset of the data for prediction purposes. In this paper, we propose a new distance-based spatial RBFs method which allows modeling spatial continuous random variables. The trend is incorporated into a RBF according to a detrending procedure with mixed variables, among which we may have categorical variables. In order to evaluate the efficiency of the proposed method, a simulation study is carried out for a variety of practical scenarios for five distinct RBFs, incorporating principal coordinates. Finally, the proposed method is illustrated with an application of prediction of calcium concentration measured at a depth of 0-20 cm in Brazil, selecting the smoothing parameter by cross-validation.