Rudolf Duenki: Robuste Variogrammschätzung und robustes Kriging

Adviser: Prof. Dr. H.R. Künsch

August 2009


Abstract:

The thesis describes the development of robust algorithms for the analysis of geostatistical data. Three algorithms where implemented in R and each of these allows for a simultaneous estimation of the regression parameters and the covariance parameters. All three algorithms returned consistent results. Two of them are implemented as a package of R-functions. The treatment of the nugget effect makes the essential difference between the two algorithms: the first algorithm treats the nugget as a part of the estimation of the covariance parameters. The other algorithm treats the nugget as a part of the regression problem. This bears advantages in the analysis of polluted data.

Sets of 50 simulations with different degrees of added pollution were analysed. The resulting parameter estimates agreed with the true values within the statistically tolerable range. The exception was the set containing the most polluted data. The estimation of the range parameter was somewhat problematic when performed with small Huber constants i.e. the resulting range displayed a bias upward. In contrast to this, the nugget estimate was improved when choosing a small Huber constant. The algorithm treating the nugget effect as a part of the regression problem returned more stable results in the case of a high degree of pollution. A Huber constant of 1.333 ... 1.666 appeared appropriate in these cases. An increase in stability was also visible in the behaviour of influence functions.
The algorithms were applied to data on contamination of soils with Cu in the surroundings of a metal smelter in Dornach. It could be shown that the estimated parameters allowed for kriging estimates which are comparable with earlier analyses. Despite this it was not possible to gain unambigous parameter estimates. The reason lies in the existence of a very flat and extended optimum region. This allows for fitting models with comparable goodness of fit characteristics for clearly distinct parameter sets.  

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