The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Data-Dependent Choice of Optimal Number of Lags in Variogram Estimation

  • Choi, Seung-Bae (Department of Data Information Science, Dongeui University) ;
  • Kang, Chang-Wan (Department of Data Information Science, Dongeui University) ;
  • Cho, Jang-Sik (Department of Information Statistics, Kyungsung University)
  • Received : 20100300
  • Accepted : 20100400
  • Published : 2010.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

Geostatistical data among spatial data is analyzed in three stages: (1) variogram estimation, (2) model fitting for the estimated variograms and (3) spatial prediction using the fitted variogram model. It is very important to estimate the variograms properly as the first stage(i.e., variogram estimation) affects the next two stages. In general, the variogram is estimated with the moment estimator. To estimate the variogram, we have to decide the 'lag increment' or the 'number of lags'. However, there is no established rule for selecting the number of lags in estimating the variogram. The present paper proposes a method of choosing the optimal number of lags based on the PRESS statistic. To show the usefulness of the proposed method, we perform a small simulation study and show an empirical example with with air pollution data from Korea.

Keywords

References

  1. Cressie, N. A. C. (1991). Statistics for Spatial, Wiley, New York.
  2. Isaaks, E. H. and Srivastava, R. M. (1989). An Introduction to Applied Geostatistics, Oxford University Press, New York.
  3. Istok, J. D. and Cooper, R. M. (1988). Geostatistics applied to ground water pollution III: Global estimates, Journal of Environmental Engineering, 114, 915-928. https://doi.org/10.1061/(ASCE)0733-9372(1988)114:4(915)
  4. Journel, A. G. (1984). New ways of assessing spatial distribution of pollutants, In Environmental Sampling for Hazardous Waters, G. Schweitzer(Ed.), 109-118. American Chemical Society, Washington.
  5. Journel, A. G. and Huijbregts, C. J. (1978). Mining Geostatistics, Academic Press, London.
  6. Matheron, G. (1963). Principles of Geostatistics, Economic Geostatistics, Academic Press, London.
  7. MathSoft Inc. (1996). S+SPATIALSTATS User's manual, MathSoft Inc., Seattle, Washington.
  8. Myers, D. E. (1984). Borden field data and multivariate geostatistics In Hydraulic Engineering, M. A. Ports(Ed.), 795-800. American Society of Civil Engineering, NewYork.
  9. Piazza, A., Menozzi, P. and Cavalli-Sforza, L. (1981). The making and testing of geographic gene frequency maps, Biometrics, 37, 635-659. https://doi.org/10.2307/2530147
  10. SAS Institute Inc. (1998). SAS/STAT Technical Report: Spatial Prediction Using the SAS System, SAS Institute Inc..
  11. Webster, R. (1985). Quantitative spatial analysis of soil in the field, In Advances in Soil Science, 3, B. A. Stewart(ed.), 1-70. Springer-Verlag, New York.
  12. Zimmerman, D. L. and Zimmerman, M. B. (1991). A comparison of spatial semivariogram estimators and corresponding ordinary kriging predictors, Technometrics, 33, 77-92. https://doi.org/10.2307/1269009