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Statistical Methods & Applications

, Volume 23, Issue 2, pp 149–174 | Cite as

Estimation of covariance functions by a fully data-driven model selection procedure and its application to Kriging spatial interpolation of real rainfall data

  • Rolando Biscay Lirio
  • Dunia Giniebra Camejo
  • Jean-Michel LoubesEmail author
  • Lilian Muñiz Alvarez
Article

Abstract

In this paper, we propose a data-driven model selection approach for the nonparametric estimation of covariance functions under very general moments assumptions on the stochastic process. Observing i.i.d replications of the process at fixed observation points, we select the best estimator among a set of candidates using a penalized least squares estimation procedure with a fully data-driven penalty function, extending the work in Bigot et al. (Electron J Stat 4:822–855, 2010). We then provide a practical application of this estimate for a Kriging interpolation procedure to forecast rainfall data.

Keywords

Model selection Covariance estimation Kriging method 

Mathematics Subject Classification (2000)

62G05 62G20 

Notes

Acknowledgments

The authors would like to thank the referees for their valuable comments.

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Rolando Biscay Lirio
    • 1
  • Dunia Giniebra Camejo
    • 2
  • Jean-Michel Loubes
    • 3
    Email author
  • Lilian Muñiz Alvarez
    • 4
  1. 1.Facultad de Ingeniería, CIMFAVUniversidad de ValparaísoValparaisoChile
  2. 2.Instituto de Cibernética, Matemática y FísicaHavanaCuba
  3. 3.Institut de Mathématiques de ToulouseToulouseFrance
  4. 4.Facultad de Matemática y ComputaciónUniversidad de La HabanaHavanaCuba

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