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| Titel |
Robust geostatistical analysis of spatial data |
| VerfasserIn |
A. Papritz, H. R. Künsch, C. Schwierz, W. A. Stahel |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250061013
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| Zusammenfassung |
| Most of the geostatistical software tools rely on non-robust algorithms. This is
unfortunate, because outlying observations are rather the rule than the exception,
in particular in environmental data sets. Outlying observations may results from
errors (e.g. in data transcription) or from local perturbations in the processes that
are responsible for a given pattern of spatial variation. As an example, the spatial
distribution of some trace metal in the soils of a region may be distorted by emissions
of local anthropogenic sources. Outliers affect the modelling of the large-scale
spatial variation, the so-called external drift or trend, the estimation of the spatial
dependence of the residual variation and the predictions by kriging. Identifying
outliers manually is cumbersome and requires expertise because one needs parameter
estimates to decide which observation is a potential outlier. Moreover, inference
after the rejection of some observations is problematic. A better approach is to use
robust algorithms that prevent automatically that outlying observations have undue
influence.
Former studies on robust geostatistics focused on robust estimation of the sample
variogram and ordinary kriging without external drift. Furthermore, Richardson and Welsh
(1995) [2] proposed a robustified version of (restricted) maximum likelihood ([RE]ML)
estimation for the variance components of a linear mixed model, which was later used
by Marchant and Lark (2007) [1] for robust REML estimation of the variogram.
We propose here a novel method for robust REML estimation of the variogram
of a Gaussian random field that is possibly contaminated by independent errors
from a long-tailed distribution. It is based on robustification of estimating equations
for the Gaussian REML estimation. Besides robust estimates of the parameters of
the external drift and of the variogram, the method also provides standard errors
for the estimated parameters, robustified kriging predictions at both sampled and
unsampled locations and kriging variances. The method has been implemented in an R
package.
Apart from presenting our modelling framework, we shall present selected simulation
results by which we explored the properties of the new method. This will be complemented
by an analysis of the Tarrawarra soil moisture data set [3].
References
[1]   Marchant, B. P. and Lark, R. M. (2007). Robust estimation of the variogram
by residual maximum likelihood. Geoderma, 140, 62–72.
[2]   Richardson, A. M. and Welsh, A. H. (1995). Robust restricted maximum
likelihood in mixed linear models. Biometrics, 51, 1429–1439.
[3]   Western, A. W. and Grayson, R. B. (1998). The Tarrawarra data set: Soil
moisture patterns, soil characteristics, and hydrological flux measurements. Water
Resources Research, 34(10), 2765–2768. |
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