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Nonparametric geostatistical risk mapping

  • Rubén Fernández-Casal
  • Sergio Castillo-Páez
  • Mario Francisco-FernándezEmail author
Original Paper

Abstract

In this work, a fully nonparametric geostatistical approach to estimate threshold exceeding probabilities is proposed. To estimate the large-scale variability (spatial trend) of the process, the nonparametric local linear regression estimator, with the bandwidth selected by a method that takes the spatial dependence into account, is used. A bias-corrected nonparametric estimator of the variogram, obtained from the nonparametric residuals, is proposed to estimate the small-scale variability. Finally, a bootstrap algorithm is designed to estimate the unconditional probabilities of exceeding a threshold value at any location. The behavior of this approach is evaluated through simulation and with an application to a real data set.

Keywords

Local linear regression Nonparametric estimation Kriging Bias-corrected variogram estimation Bootstrap 

Notes

Acknowledgements

The research of Rubén Fernández-Casal and Mario Francisco-Fernández has been partially supported by the Consellería de Cultura, Educación e Ordenación Universitaria of the Xunta de Galicia through the agreement for the Singular Research Center CITIC, and by Grant MTM2014-52876-R. The research of Sergio Castillo has been partially supported by the Universidad de las Fuerzas Armadas ESPE, from Ecuador. The authors thank the associate editor and two referees for constructive comments that improved the presentation of this article.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Departamento de Matemáticas, Facultad de InformáticaUniversidade da CoruñaA CoruñaSpain
  2. 2.Departamento de Estadística e Investigación OperativaUniversidad de VigoVigoSpain
  3. 3.Universidad de las Fuerzas Armadas ESPESangolquíEcuador

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