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Use of the Jackknife Method to Estimate Autocorrelation Functions (or Variograms)

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Abstract

An application of the jackknife method to estimate autocorrelation functions (or variograms) of stationary random functions is discussed. Using the jackknife estimators and the corresponding jackknife variances, the models of the autocorrelation functions are fitted by the weighted least squares method. The method is particularly effective to study robustness of the estimators when the number of data points is small. The technique is applied to simulated data sets with known autocorrelation functions.

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References

  1. Agterberg, F. P., 1970, Autocorrelation functions in geology, Geostatistics, Ed. D. F. Merriam, Plenum Press, pp. 113–141.

    Google Scholar 

  2. Andrews, D. F., Bickel, P. J., Hampel, F. R., Hubel,P. J., Rogers, W. H., Tukey, J. W., 1972, Robust Estimates of Location, Princeton Univ. Press, 371 p.

    Google Scholar 

  3. Cressie, N and Hawkins, D. M., 1980, Robust estimation of the variogram: I, Math. Geology, V. 12, N. 2, pp. 115–125.

    Article  Google Scholar 

  4. Draper, N. R. and Smith, H., 1968, Applied Regression Analysis, Wiley, 407 pp.

    Google Scholar 

  5. Huijbregts, Ch., 1971, Reconstitution du variogramme ponctuel a partir d’un variogramme experimental regularize, Ecole de Mines de Paris, 26 pp.

    Google Scholar 

  6. Johnson, N. L. and Kotz, S., 1970, Continuous Univariate Distributins-2, Houghton Miffin, Chapter 32, p. 220–252.

    Google Scholar 

  7. Johnson, N. L. and Kotz, S., 1972, Continuous Multivariate distributions, John Wiley, Chapter 35, p37–83.

    Google Scholar 

  8. Jowett, G. H., 1955, Least squares regression analysis for trend-reduced time-series, J.R.S.S., Ser. B, V. 17, pp. 91–104.

    Google Scholar 

  9. Kendall, M. G., 1973, Time-series, Griffin, 197 pp.

    Google Scholar 

  10. Matheron, G., 1962, Traite de Geostatistique Appliquee, Tome 1, Editions Technip, Paris.

    Google Scholar 

  11. Matheron, G., 1971, The Theory of Regionalized Variables and its applications, Ecole de Mines de Paris, Paris, 211 pp.

    Google Scholar 

  12. Mosteller, F, 1971, The jackknife, Rev. Int. Stat. Inst., V. 39, pp. 363–368.

    Article  Google Scholar 

  13. Quenoui1le, M., 1956, Notes on bias in estimation, Biometrika, V. 43, pp. 353–360.

    Google Scholar 

  14. Robinson, B., 1979, SPSS Subprogram NONLINEAR-Nonlinear Regression, Vogelback Comp. C. Manual N. 433, 27 pp.

    Google Scholar 

  15. Tukey, J. W., 1958, Bias and confidence in not quite large samples, Ann. Math. Stat., V. 29, pp. 614.

    Article  Google Scholar 

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© 1984 D. Reidel Publishing Company

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Chung, C.F. (1984). Use of the Jackknife Method to Estimate Autocorrelation Functions (or Variograms). In: Verly, G., David, M., Journel, A.G., Marechal, A. (eds) Geostatistics for Natural Resources Characterization. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3699-7_4

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  • DOI: https://doi.org/10.1007/978-94-009-3699-7_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8157-3

  • Online ISBN: 978-94-009-3699-7

  • eBook Packages: Springer Book Archive

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