Skip to main content
Log in

M-Estimator of the drift coefficients in a spatial linear model

  • Published:
Mathematical Geology Aims and scope Submit manuscript

Abstract

Kriging as an interpolation method, uses as predictor a linear function of the observations, minimizing the mean squared prediction error or estimation variance. Under multivariate normality assumptions, the given predictor is the best unbiased predictor, and will be vulnerable to outliers. To overcome this problem, a robust weighted estimator of the drift model coefficients is proposed, where unequally spaced data may be weighted through the tile areas of the Dirichlet tessellation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Cook, D. G., and Pocock, S. J., 1983, Multiple regression in geographic mortality studies with allowance for spatially correlated errors: Biometrics, v. 39, no. 2. p. 361–371.

    Article  Google Scholar 

  • Cressie, N., 1985, Fitting variogram models by weighted least squares: Math. Geology, v. 17, no. 5, p. 563–586.

    Article  Google Scholar 

  • Cressie, N., and Hawkins, D. M., 1980, Robust estimation of the variogram: Math. Geology, v. 12, no. 2, p. 115–125.

    Article  Google Scholar 

  • Davis, J. C., 1986, Statistics and data analysis in geology (2nd ed.): John Wiley & Sons, New York, 646 p.

    Google Scholar 

  • Green, P. J., and Sibson, R., 1978, Computing Dirichlet tessellations in the plane: Computer Jour., v. 21, no. 2, p. 168–173.

    Google Scholar 

  • Handcock, M. S., and Stein, M. L., 1993, A bayesian analysis of kriging: Technometrics, v. 35, no. 4, p. 403–410.

    Article  Google Scholar 

  • Hawkins, D. M., and Cressie, N., 1984, Robust kriging: a proposal: Math. Geology, v. 16, no. 1, p. 3–18.

    Article  Google Scholar 

  • Huber, P. J., 1981, Robust statistics: Wiley Series in Probability and Mathematical Statistics, New York, 308 p.

    Google Scholar 

  • Mardia, K. V., and Marshall, R. J., 1984, Maximum likelihood estimation of models for residual covariance in spatial regression: Biometrika, v. 71, no. 1, p. 135–146.

    Article  Google Scholar 

  • Mardia, K. V., and Watkins, A. J., 1989, On multimodality of the likelihood in the spatial linear model: Biometrika, v. 76, no. 2, p. 289–295.

    Article  Google Scholar 

  • Ripley, B. D., 1981, Spatial statistics: Wiley Series in Probability and Mathematical Statistics, New York, 252 p.

    Google Scholar 

  • Ripley, B. D., 1988, Statistical inference for spatial processes: Cambridge Univ. Press, Cambridge, 148 p.

    Google Scholar 

  • S-Plus, 1994, S-Plus for windows, user’s manual vol. I: Statistical Sciences, Seattle, Washington, 437 p.

    Google Scholar 

  • Staudte, R. G., and Sheather, S. J., 1990, Robust estimation and testing: Wiley Series in Probability and Mathematical Statistics, New York, 351 p.

    Google Scholar 

  • Stone, M., 1974, Cross-validatory choice and assessment of statistical predictions: Jour. Roy. Stat. Soc., Ser. B, v. 36, no. 2, p. 111–147.

    Google Scholar 

  • Venables, W. N., and Ripley, B. D., 1994, Modern applied statistics with S-Plus: statistics and computing: Springer-Verlag, New York, 462 p.

    Google Scholar 

  • Wames, J. J., 1986, A sensitivity analysis for universal kriging: Math. Geology, v. 18, no. 7, p. 653–676.

    Google Scholar 

  • Warnes, J. J., and Ripley, B. D., 1987, Problems with likelihood estimation of covariance functions of spatial gaussian processes: Biometrika, v. 74, no. 3, p. 640–642.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ana F. Militino.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Militino, A.F. M-Estimator of the drift coefficients in a spatial linear model. Math Geol 29, 221–229 (1997). https://doi.org/10.1007/BF02769629

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02769629

Key Words

Navigation