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

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Listed:
  • Rolando Biscay Lirio
  • Dunia Camejo
  • Jean-Michel Loubes
  • Lilian Muñiz Alvarez

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Rolando Biscay Lirio & Dunia Camejo & Jean-Michel Loubes & Lilian Muñiz Alvarez, 2014. "Estimation of covariance functions by a fully data-driven model selection procedure and its application to Kriging spatial interpolation of real rainfall data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 149-174, June.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:2:p:149-174
    DOI: 10.1007/s10260-013-0250-7
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    References listed on IDEAS

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    1. Shapiro, A. & Botha, J. D., 1991. "Variogram fitting with a general class of conditionally nonnegative definite functions," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 87-96, January.
    2. Matsuo, Tomoko & Nychka, Douglas W. & Paul, Debashis, 2011. "Nonstationary covariance modeling for incomplete data: Monte Carlo EM approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2059-2073, June.
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