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Notes on the robustness of the kriging system

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Abstract

The robustness of the kriging system with respect to uncertainty of the theoretical variogram is investigated. Inequalities for possible changes of the kriging estimator and the estimation variance are derived. Results of a numerical study show that changes of kriging weights can be predicted partly with the help of the maximal kriging weight.

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References

  1. Akhiezer, N. I. and Glazmann, I. M., 1981,Theory of Linear Operators in Hilbert Space, Vol. I.: Pitman Publishing, Boston, p. 312.

  2. Armstrong, M., 1984, Improving the Estimation and Modeling of the Variogram,in Verly et al. (Eds.),Geostatistics for Natural Resources Characterization: D. Reidel, Amsterdam, p. 1–19.

  3. Brooker, P. I., 1986, A Parametric Study of Robustness of Kriging Variance as a Function of Range and Relative Nugget Effect for a Spherical Semivariogram:Math Geol, v. 18, no. 5, p. 477–488.

  4. Cressie, N. and Hawkins, D., 1980, Robust Estimation of the Variogram, I:Math Geol., v. 12, no. 2, p. 115–125.

  5. Diamond, P. and M. Armstrong, 1984, Robustness of Variograms and conditioning of Kriging Matrices:Math Geol, v. 16, no. 8, p. 809–822.

  6. Dowd, P. A., 1984, The Variogram and Kriging: Robust and Resistant Estimators,in Verly et al. (Eds.),Geostatistics for Natural Resources Characterization: D. Reidel, Amsterdam, p. 91–106.

  7. Omre, H., 1984, The Variogram and its Estimation,in Verly et al. (Eds.),Geostatistics for Natural Resources Characterization: D. Reidel, Amsterdam, p. 107–125.

  8. Journel, A. and Ch. Hiujbregts, 1978,Mining Geostatistics: Academic Press, New York, 600 p.

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Bardossy, A. Notes on the robustness of the kriging system. Math Geol 20, 189–203 (1988). https://doi.org/10.1007/BF00890253

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Key words

  • kriging
  • variogram
  • robustness
  • estimation variance