Spatial Breakdown Point of Variogram Estimators

In the context of robust statistics, the breakdown point of an estimator is an important feature of reliability. It measures the highest fraction of contamination in the data that an estimator can support before being destroyed. In geostatistics, variogram estimators are based on spatially located data sets. Therefore, the classical notion of breakdown point needs to be extended to a spatial one, depending on the construction of most unfavorable configurations of perturbation. Explicit upper and lower bounds are available for the spatial breakdown point in the unidimensional case. The difficulties arising in the multidimensional case are presented on an easy example in R2. In order to study the effects of perturbations, several simulations are carried out on data located on a regular or irregular bidimensional grid. Results show that if variogram estimation is performed with a 50% classical breakdown point scale estimator, then the number of initial data likely to be contaminated before destruction of the estimator is roughly 30% in average. Theoretical results confirm the previous statement on data in Rd, d>1.