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

Author

Listed:
  • Carlos E. Melo

    (Universidad Distrital Francisco José de Caldas)

  • Oscar O. Melo

    (Universidad Nacional de Colombia)

  • Jorge Mateu

    (University Jaume I)

Abstract

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.

Suggested Citation

  • Carlos E. Melo & Oscar O. Melo & Jorge Mateu, 2018. "A distance-based model for spatial prediction using radial basis functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 263-288, April.
    • Handle: RePEc:spr:alstar:v:102:y:2018:i:2:d:10.1007_s10182-017-0305-4
    DOI: 10.1007/s10182-017-0305-4
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    References listed on IDEAS

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    1. Guoyi Zhang, 2012. "Smoothing splines using compactly supported, positive definite, radial basis functions," Computational Statistics, Springer, vol. 27(3), pages 573-584, September.
    2. M. P. Wand, 2000. "A Comparison of Regression Spline Smoothing Procedures," Computational Statistics, Springer, vol. 15(4), pages 443-462, December.
    3. Hüseyin Yavuz & Saffet Erdoğan, 2012. "Spatial Analysis of Monthly and Annual Precipitation Trends in Turkey," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(3), pages 609-621, February.
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