Robust Resampling Confidence Intervals for Empirical Variograms
- 226 Downloads
The variogram function is an important measure of the spatial dependencies of a geostatistical or other spatial dataset. It plays a central role in kriging, designing spatial studies, and in understanding the spatial properties of geological and environmental phenomena. It is therefore important to understand the variability attached to estimates of the variogram. Existing methods for constructing confidence intervals around the empirical variogram either rely on strong assumptions, such as normality or known variogram function, or are based on resampling blocks and subject to edge effect biases. This paper proposes two new procedures for addressing these concerns: a quasi-block-bootstrap and a quasi-block-jackknife. The new methods are based on transforming the data to decorrelate it based on a fitted variogram model, resampling blocks from the decorrelated data, and then recorrelating. The coverage properties of the new confidence intervals are compared by simulation to a number of existing resampling-based intervals. The proposed quasi-block-jackknife confidence interval is found to have the best properties of all of the methods considered across a range of scenarios, including normally and lognormally distributed data and misspecification of the variogram function used to decorrelate the data.
KeywordsSpatial analysis Variograms Bootstrap Jackknife Block bootstrap Block jackknife
Unable to display preview. Download preview PDF.
- Chiles J-P, Delfiner P (1999) Geostatistics: Modelling spatial uncertainty. Wiley, New York Google Scholar
- Cressie N (1993) Statistics for spatial data. Wiley, New York Google Scholar
- Davison A, Hinkley D (1997) Bootstrap methods and their application. Cambridge University Press, Cambridge Google Scholar
- Dowd P (1984) The variogram and kriging: robust and resistant estimators. In: Geostatistics for natural resource characterization. Reidel, Dordrecht, pp 91–106 Google Scholar
- Huisman J, Snepvangers J, Bouten W, Heuvelink G (2003) Monitoring temporal development of spatial soil water content variation: comparison of ground penetrating radar and time domain reflectometry. Vadose Zone J 2(4):519–529 Google Scholar
- Kunsch HR (1989) The jackknife and the bootstrap for general stationary observations. Ann Math Stat 17(3):1217–1241 Google Scholar
- Lahiri S (2003) Resampling methods for dependent data. Springer, New York Google Scholar
- Oliver M, Webster R (2001) Geostatistics for environmental scientists. Wiley, Chichester Google Scholar
- R Development Core Team (2007) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. ISBN 3-900051-07-0 Google Scholar
- Schlather M (2006) RandomFields: Simulation and analysis of random fields. R package version 1.3.29 Google Scholar
- Tang L, Schucany W, Woodward W, Gunst R (2006) A parametric spatial bootstrap. Technical Report SMU-TR-337, Southern Methodist University, Dallas, Texas Google Scholar