Advertisement

Mathematical Geology

, Volume 33, Issue 6, pp 679–691 | Cite as

Fixed-Domain Asymptotics for Variograms Using Subsampling

  • Montserrat Fuentes
Article

Abstract

The variogram is a measure of the local variation in space of a random field. For large geostatistical data sets, the traditional empirical variogram may be hard to compute. This article presents, for processes with a fixed domain, the effect of using a subsample of the available data on the performance of the empirical variogram. The motivation of this work, apart from the saving on computation, is to study how dense the observations need to be in the bounded sampling region to obtain most of the information we would get from continuous observations in the fixed domain.

empirical variogram fixed domain geostatistics infill asymptotics spatial statistics subsampling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Becker, R. A., and Cleveland, W. S., 1996, The design and control of Trellis displays: Journal of Computational and Graphical Statistics, v. 5, p. 123–155.Google Scholar
  2. Chilès, J. P., and Delfiner, P., 1999, Geostatistics, Modeling Spatial Uncertainty: Wiley, New York.Google Scholar
  3. Clayton, M. K., and Hudelson, B. D., 1995, Confidence intervals for autocorrelations based on cyclic samples: Jour. of the Am. Stat. Assoc., v. 90, p. 753–757.Google Scholar
  4. Clinger, W., and Van Ness, J.W., 1976, On unequally spaced time points in time series: The Annals of Statistics, v. 4, p. 736–745.Google Scholar
  5. Cressie, N. A. C., 1993, Statistics for Spatial Data, revised edition: John Wiley & Sons, New York.Google Scholar
  6. Kaiser, M. S., Hsu, N., Cressie, N., and Lahiri, S. N., 1997, Inference for spatial processes using subsampling: A simulation study: Environmetrics, v. 8, p. 485–502.Google Scholar
  7. Lahiri, S. N., 1995, Asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling method: Department of Statistics, Iowa State University, Ames, IA.Google Scholar
  8. Marcotte, D., 1996, Fast variogram computation with FFT: Computers & Geoscience, v. 22, p. 1175-1186.Google Scholar
  9. Matheron, G., 1971, The theory of regionalized variables and its applications: Les Cahiers du Centre de Morphologie Mathématique, Fasc. 5, Centre de Géostatistique, Fontainebleau.Google Scholar
  10. Matheron, G., 1989, Estimating and choosing: Springer, Berlin.Google Scholar
  11. Morris, M. D., and Edey, S. F., 1984, Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, v. 38, p. 127–129.Google Scholar
  12. Peppler, R. A., and Lamb, P. J., 1996, Site scientific mission plan for the SGP CART site. ARM-96001, U.S. Department of Energy, Office of Energy Research, Office of Health and Environmental Research, Environmental Sciences Division.Google Scholar
  13. Priestly, M. B., 1981, Spectral analysis and time series: Academic Press, New York.Google Scholar
  14. Sisterson, D., Wesely, M., and Eagan, R., 1994, Climate change characterized at research home on the range: Logos—Argonne National Laboratory, v. 12, no. 1.Google Scholar
  15. Stein, M. L., 1987, Minimum norm quadratic estimation of spatial variograms: Jour. of the Am. Stat. Assoc., v. 82, p. 765–772.Google Scholar
  16. Stein, M. L., 1990, Bounds on the efficiency of linear predictions using and incorrect covariance function: The Annals of Statistics, v. 18, p. 1116–1138.Google Scholar
  17. Stein, M. L., 1993, A simple condition for asymptotic optimality of linear predictions of random fields: Statistics and Probability Letters, v. 17, p. 399–414.Google Scholar
  18. Stein, M. L., 1995, Fixed-domain asymptotics for spatial periodograms: Jour. of the Am. Stat. Assoc. v. 90, p. 1277–1288.Google Scholar

Copyright information

© International Association for Mathematical Geology 2001

Authors and Affiliations

  • Montserrat Fuentes
    • 1
  1. 1.Department of StatisticsNorth Carolina State UniversityRaleigh

Personalised recommendations