Spatial Variability in Slash Linear Modeling with Finite Second Moment

  • R. S. Fagundes
  • M. A. Uribe-Opazo
  • M. Galea
  • L. P. C. Guedes


This article studies the dependence of spatial linear models using a slash distribution with a finite second moment. The parameters of the model are estimated with maximum likelihood by using the EM algorithm. To avoid identifiability problems, the cross-validation, the Trace and the maximum log-likelihood value are used to choose the parameter for adjusting the kurtosis of the slash distribution and the selection of the model to explain the spatial dependence. We present diagnostic techniques of global and local influences for exploring the sensibility of estimators and the presence of possible influential observations. A simulation study is developed to determine the performance of the methodology. The results showed the effectiveness of the choice criteria of the parameter for adjusting the kurtosis and for the selection of the spatial dependence model. It has also showed that the slash distribution provides an increased robustness to the presence of influential observations. As an illustration, the proposed model and its diagnostics are used to analyze an aquifer data. The spatial prediction with and without the influential observations were compared. The results show that the contours of the interpolation maps and prediction standard error maps showed low changes when we removed the influential observations. Thus, this model is a robust alternative in the spatial linear modeling for dependent random variables. Supplementary materials accompanying this paper appear online.


EM algorithm Analysis of spatial data Geostatistics Global and local influence Robust modeling 



Funding was provided by Capes, Fundação Araucária, CNPq Brazil, FONDECYT (Grant No. 1150325).

Supplementary material

13253_2018_322_MOESM1_ESM.pdf (193 kb)
Supplementary material 1 (pdf 193 KB)
13253_2018_322_MOESM2_ESM.pdf (1.5 mb)
Supplementary material 2 (pdf 1564 KB)


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Copyright information

© International Biometric Society 2018

Authors and Affiliations

  • R. S. Fagundes
    • 1
  • M. A. Uribe-Opazo
    • 2
  • M. Galea
    • 3
  • L. P. C. Guedes
    • 2
  1. 1.Federal Technological University of ParanáToledoBrazil
  2. 2.Western Paraná State UniversityCascavelBrazil
  3. 3.Departamento de EstadísticaPontificia Universidad Católica de ChileMaculChile

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