AStA Advances in Statistical Analysis

, Volume 102, Issue 2, pp 263–288 | Cite as

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

  • Carlos E. Melo
  • Oscar O. Melo
  • Jorge Mateu
Original Paper


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.


Detrending Distance-based methods Radial basis functions Random function models Smoothing parameter Spatial prediction 



Work partially funded and supported by: Grant MTM2016-78917-R from the Spanish Ministry of Science and Education; Core Spatial Data Research (Faculty of Engineering, Francisco José de Caldas District University) (Grant COL0013969); and Applied Statistics in Experimental Research, Industry and Biotechnology (Universidad Nacional de Colombia) (Grant COL0004469).

Supplementary material

10182_2017_305_MOESM1_ESM.r (25 kb)
Supplementary material 1 (R 25 KB)
10182_2017_305_MOESM2_ESM.r (69 kb)
Supplementary material 2 (R 68 KB)


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Faculty of EngineeringUniversidad Distrital Francisco José de CaldasBogotáColombia
  2. 2.Department of Statistics, Faculty of SciencesUniversidad Nacional de ColombiaBogotáColombia
  3. 3.Department of MathematicsUniversity Jaume ICastellón de la PlanaSpain

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